LABORATORY   EXERCISES 


IN 


ELEMENTARY  PHYSICS 


BY  i/ 

CHARLES  R.  ALLEN,  S.B.'"L 

Instructor  in  the  New  Bedford,  Mass.,  High  School 


NEW  YORK 
HENRY    HOLT    AND    COMPANY 

1895 


COPYRIGHT,  1893, 

BY 
HENRY  HOLT  &  CO. 


ROBERT  DRUMMOND, 

ELECTROTYPER  AND  PRINTER, 

NEW  YORK. 


Add  to  Lib. 


PREFACE. 


MOST  of  the  experiments  in  this  collection  exact  of  the 
pupil  measurements  of  some  sort,  that  is,  are  quantitive. 
A  few,  included  for  the  training  in  accurate  work  they 
afford  or  for  their  suggestiveness,  demand  the  investigations 
of  the  conditions  under  which  certain  phenomena  develop. 
They  require,  however,  the  use  of  some  physical  instrument. 
Those  purely  illustrative  are  given  because  they  demand 
more  careful  observation  than  the  pupil  can  give  to  a  lec- 
ture experiment.  In  the  course  will  be  found,  I  think, 
illustrations  of  many  of  the  more  common  methods  of 
physical  research.  The  exercises  are  planned  for  young 
pupils  with  no  previous  training  in  physics,  employ  no  un- 
duly expensive  apparatus,  and  require  no  more  than  forty- 
five  minutes  each  in  the  laboratory.  The  subjects  selected 
are  among  those  bearing  on  the  commoner  applications  of 
physical  science.  Pains  have  been  taken  to  so  frame  the 
instructions  that  the  pupil  can  prepare  himself  beforehand 
to  make  the  most  of  his  laboratory  time  with  the  least  help 
from  his  instructor.  This  I  regard  of  prime  importance. 
Unless  the  instructor  assures  himself  before  each  exercise 
that  the  pupils  understand  what  they  are  to  do  and  how  to 
do  it,  they  will  pretty  surely  exceed  the  time-limit,  and  may 
even  make  wreck  of  the  whole  exercise.  Five  unprepared 
pupils  require  more  attention  than  fifteen  who  have  thor- 
oughly mastered  the  preliminary  work.  When  entirely 
new  or  especially  complicated  apparatus  is  to  be  used,  I 

iii 


iv  PREFACE. 

find  it  advisable  to  place  a  "  dummy"  set  before  the  class, 
and  spend  part  or  the  whole  of  one  period  in  requiring 
individual  pupils  to  go  through  the  motions  with  it,  to 
answer  questions  on  the  general  method  and  the  special 
manipulations,  and,  in  case  of  a  complicated  calculation, 
to  work  out  results  from  imaginary  data. 

The  arrangement  and  even  the  phrasing  of  the  ma- 
terial is  the  outgrowth  of  much  searching  for  a  general 
form  which  would  be  most  effective  in  stimulating  clear 
and  independent  thinking.  Each  exercise  is  introduced 
by  some  preliminary  explanation  and  a  distinct  statement 
of  its  object.  This  puts  before  the  pupil  the  precise  thing 
he  is  after,  and  the  general  course  of  his  investigation. 
The  manipulation  is  then  described  with  what  some  may 
deem  unnecessary  minuteness,  but  I  find  this  minuteness 
part  of  the  secret  of  speed  and  success.  I  have  added  ques- 
tions where  I  have  found  them  convenient  in  guiding  the 
pupils'  thought,  but  in  no  instance,  I  believe,  do  they  con- 
tain their  own  answer.  In  a  few  cases  I  have  given  alter- 
native exercises  on  the  same  topic,  for  the  purpose  of 
suiting  the  varying  experimental  aptitude  of  pupils. 

In  the  order  of  subjects,  the  exercises  form  a  somewhat 
roughly  graded  course,  from  magnetic  phenomena,  where 
work  is  simplest  and  most  stimulative  to  attention,  through 
experiments  involving  the  measurement  of  a  single  value 
by  means  of  some  single  instrument,  to  the  more  compli- 
cated quantitive  determinations  of  Dynamics.  This  order 
places  the  most  difficult  part  of  Physics  last,  where  the 
pupil  can  bring  to  his  aid,  in  grasping  abstract  ideas  and 
performing  intricate  experiments,  the  training  acquired  in 
the  previous  parts  of  the  course.  But  since  the  instruc- 
tions in  one  subject  do  not  assume  a  previous  knowledge 
of  any  other,  there  is  nothing  to  prevent  the  subjects  being 
taken  up  in  any  order  desired,  though  of  course  practice 
in  mensuration  should  precede  the  quantitive  exercises. 


PREFACE.  V 

The  book  is  made  up  mainly  of  the  author's  instructions 
to  his  own  pupils  for  their  laboratory  work.  The  course 
of  which  this  forms  a  part  includes  also  the  performance 
of  all  necessary  descriptive  experiments  before  the  class, 
and  the  use  of  a  text-book.  Before  the  pupil  goes  to  work 
in  the  laboratory  at  all,  he  should  be  given  a  general  idea 
of  how  knowledge  is  acquired  experimentally,  and  the  steps 
involved  in  carrying  on  an  experimental  investigation. 
The  instruction  on  these  points  should  be  illustrated  by 
some  simple  typical  experiments  by  the  teacher.  After- 
wards the  relative  order  of  text-book  and  laboratory  work 
will  naturally  depend  upon  the  nature  of  the  laboratory 
exercises.  In  exercises  involving  the  study  of  conditions, 
as  in  those  on  Magnetism,  and  some  of  those  on  Electricity 
and  Heat,  the  author  prefers  that  the  laboratory  work  pre- 
cede the  text-book  work;  but  in  exercises  involving  definite 
measurement,  as  in  Specific  Gravity  and  Specific  Heat,  this 
order  may  well  be  reversed.  Certainly,  in  the  investiga- 
tion of  a  physical  law  by  measurements  of  two  values,  as  in 
the  exercises  on  Elasticity  or  on  the  Pendulum,  the  labora- 
tory work  should  come  first. 

In  order  to  reduce  the  volume  to  a  convenient  size  for 
the  laboratory  table,  all  matter  meant  chiefly  for  the  in- 
structor is  appended  to  the  Teachers'  Edition  and  omitted 
from  the  Pupils'  Edition,  the  two  being  identical  in  other 
respects.  Appendix  A  offers  general  suggestions  for  ar- 
ranging the  pupil's  work  and  economizing  his  and  the  in- 
structor's time,  together  with  directions  for  applying  the 
ordinary  110-volt  Edison  electric  current  to  laboratory 
work,  and  for  the  care  of  mercury.  Appendix  B  gives 
complete  lists  of  all  the  apparatus  needed  for  each  exercise, 
hints  as  to  substitutes  and  duplicates,  and  itemized  esti- 
mates of  cost  with  references  to  dealers'  catalogues.  Ap- 
pendix C  contains  full  instructions  for  making  the  more 
important  pieces  of  apparatus.  Appendix  D  furnishes 


vi  PREFACE. 

topical  references  to  Avery's  "First  Principles  of  Natural 
Philosophy"  and  "Elements  of  Natural  Philosophy/'  to 
Gage's  "Elements  of  Physics"  and  "Introduction  to  Physi- 
cal Science,"  and  to  Hall  and  Bergen's  "Text-Book  of 
Physics,"  supplemented  by  hints  on  conducting  the  vari- 
ous exercises,  the  educational  purpose  each  is  meant  to 
serve,  the  degree  of  accuracy  to  be  expected,  etc. 

While,  so  far  as  I  know,  none  of  the  experiments  will  be 
found  elsewhere  in  exactly  their  form  here,  many  have  been 
modified  from  other  manuals.  No  attempt  is  made  to 
credit  each  exercise  to  the  source  of  the  original  idea.  The 
chief  books  laid  under  contribution  are  Worthington's 
"Laboratory's  Practice,"  Stewart  and  Gee's  "Physics," 
Pickering's  "Physical  Manipulations,"  the  Harvard  College 
Course  of  Experiments,  and  Maxwell's  "  Matter  and  Mo- 
tion." The  metric  system  has  been  employed  because  it  is 
the  language  of  quantity  in  physical  laboratories,  scientific 
text-books  and  journals,  and  the  higher  scientific  manu- 
facturing processes  the  world  over.  Pupils  learn  with  such 
ease  to  use  so  much  of  it  as  this  book  requires,  that  it  forms 
no  bar  to  their  progress. 

C.  R.  A. 

NEW  BEDFORD,  MASS.,  February  1,  1892. 


CONTENTS. 


MAGNETISM. 

PAGB 

Exercise  1.  General  Study  of  a  Magnet,      .        .        .       .       .  1 

"        2.  The  Action  of  the  Attracted  Body  on  the  Magnet,  .  4 

"       3.  Mutual  Action  of  two  Magnets 6 

"        4.  Induced  Magnetism.     Breaking  Magnets,        .        .  8 

"        5.  Law  of  Induced  Magnets, 10 

"        6.  Lines  of  Magnetic  Force, 12 

CURRENT  ELECTRICITY. 

Exercise  1.  Voltaic  Electricity,  .  .  .  -  ;:  .  .  .17 
"  2.  Conditions  for  Producing  Current,  .  .  .  .20 
"  3.  Action  of  Currents  on  Magnets,  .  .  v  .  25 
'•  4.  Conditions  Affecting  Electrical  Resistance,  .  .  29 

"        5.  Electrical  Resistance, 33 

"        6.  Methods  of  Connecting  Galvanic  Cells,    .        .        .     36 

"        7.  Relative  Resistance, 40 

"        8.  A.  Measurement  of  Resistance,        .        .        .        .42 
B.  Measurement  of  Resistance,         .        .        .        .45 

"       9.  Electro-motive  Force, 48 

"      10.  Electro-magnetism,    .        ...        .        .        .        .50 

'•      11.  Induced  Currents, *       .    52 

MENSURATION. 

Notes  on  Measurement,         .        .        .        .        «        .        ,  .56 

Determination  of  Length,      .        .        ;        .        „        r        .  .59 

Exercise  1.  Practice  in  the  Use  of  Linear  Scales,        .        .  .62 

"        2.  The  Relation  of  Circumference  to  Diameter,    .  .     64 

vii 


VU1  CONTENTS. 

PAGE 

Determination  of  Volumes,  . 67 

Exercise  3.  Practice  in  Determining  Volumes,    .        .        .        .74 
"        4.  Cross-section  and  Internal  Diameter  of  a  Tube,        .     76 

Determination  of  Weight,     .        . 78 

Exercise  5.  Practice  in  Weighing, 83 

6.  Estimation  of  Metric  Values, 84 

Notes  on  Errors,    .        .        . 85 

Exercise  7.  Physical  and  Chemical  Change,        .        .        .        .86 


DENSITY  AND  SPECIFIC  GRAVITY. 

Exercise  1.  Density  and  its  Determination,  .  .  .  .89 
"  2.  Determination  of  Specific  Gravity,  .  .  .  .92 
"  3.  Weight  Lost  by  a  Body  when  Immersed  in  a  Liquid,  93 
"  4.  Specific  Gravity  by  Immersion,  .  .  .  .96 
"  5.  Liquid  Pressure  Due  to  Weight,  .  .  .  .99 
"  6.  Specific  Gravity  of  Liquids  by  Balancing,  ,  .  103 
"  7.  Weight  of  Liquid  Displaced  by  a  Floating  Body,  .  106 
"  8.  Atmospheric  Pressure  and  the  Barometer,  .  .  107 
"  9.  Specific  Gravity  of  Two  Liquids  by  Balancing 

against  Atmospheric  Pressure,      .        .        .        .109 


HEAT. 

Introductory,        ...        .        • 112 

Exercise  1.  How  Heat  Travels,    .  113 

"        2.  Testing  Thermometers 117 

"        3.  Temperature  and  Physical  Form,     .        .        .        .119 
"        4.  Laws  of  Cooling, 124 

5.  Melting  and  Boiling  Points, 125 

6.  Heat  Capacity, 127 

7.  Determination  of  Specific  Heat,        .        .        .        .128 

"       8.  Latent  Heat, .  133 

"        9.  Coefficient  of  Linear  Expansion,       .        .        .        .138 
"      10.  Cubical  Coefficient  of  a  Liquid,         .        .        .        .145 
"      11.  Coefficient  of  Expansion  of  a  Gas  at  Constant  Press- 
ure,       .        .        .      ,  .        .       .V       .        .        .  146 

"      12.  Absorption  and  Radiation, 150 

"      13.  Solution,    .    •  .'.        .        .        .        .  .        .  152 


CONTENTS.  x 

PAGE 

DYNAMICS. 

Exercise  1.  Action  of  a  Force  upon  a  Body,        .        .        .        .153 
2.  The  Force  of  Friction,      .        .        .        ;        .        .156 

"        3.  Composition  of  Forces, 160 

4.  Parallel  Forces, 166 

"        5.  The  Inclined  Plane, 169 

6.  The  Wedge  and  the  Screw,       .        .        .  .  173 

"        7.  Laws  of  the  Pendulum, 174 

"        8.  Action  and  Reaction,         ......  177 

"        9.  The  Force  of  Tenacity, .181 

"      10.  The  Force  of  Elasticity,    .        .        .        .        .  '  -    .  188 

"      11.  Boyle's  Law, 185 

"      12.  Specific  Gravity  without  Scales  or  Weights,    .        .  189 

LIGHT. 

Exercise  1.  Foci  of  Lenses, .  191 

2.  Distance  and  Intensity  of  Light,       .        .        .        .194 

3.  Radiation  of  Light, 197 

"       4.  Candle-power  by  the  Rumford  Photometer,     .        .199 

SOUND. 

Exercise  1.  Conditions  Affecting  Pitch,       .        ...        .        .201 

2.  Velocity  of  Sound, 20d 


LABORATORY  PHYSICS. 


MAGNETISM. 
EXERCISE  1. 

GENERAL  STUDY  OF  A  MAGNET. 

EXPERIMENT  1. 

Apparatus.— Bar  magnet,  a  piece  of  steel  (knife-blade  or  knitting- 
needle),  some  carpet-tacks;  pieces  of  paper,  glass,  wood,  etc.;  cop 
per  tacks;  a  piece  of  window-glass  two  or  three  inches  square;  iron- 
filings;  larger  tack  or  nail;  bottle  which  may  contain  the  iron-filings 
or  block  of  wood. 

OBJECT. — To  compare  the  results  of  bringing  first  a  piece 
of  steel  and  then  the  magnet  near  a  piece  of  iron  or 
another  piece  of  steel. 

MANIPULATION. — Bring  one  end  of  the  magnet  near  a 
few  tacks  scattered  on  a  piece  of  paper.  Observe  carefully 
what  happens.  Repeat  two  or  three  times  until  you  are 
sure  that  you  have  noticed  all  thatoccurs.  Repeat  with  an 
ordinary  piece  of  steel.  Compare  results.  Try  other 
bodies  in  place  of  the  iron.  Do  you  get  the  same  result  ? 

Definitions. — If  whenever  a  body  is  brought  near  a  piece 
of  iron  or  steel  we  obtain  the  results  observed  above,  that 
body  is  called  a  magnet.  This  name  is  given  it  not  because 
it  is  made  of  any  particular  substance  or  made  in  any  par- 
ticular shape,  but  only  because  when  placed  under  certain 
conditions,  for  instance  those  in  Experiment  1,  certain 


2  MAGNETISM. 

things  happen  that  do  not  happen  when  other  substances  are 
placed  under  the  same  conditions.  Anything  that  happens 
among  physical  things  (things  that  have  weight  or  take  up 
room)  is  called  a  physical  phenomenon  ;  for  example,  the 
behavior  of  the  tack  when  the  magnet  was  brought  near  it 
would  be  a  phenomenon.  Placing  a  body  under  certain 
conditions  and  observing  the  resultant  phenomena  is  called 
an  experiment.  A  magnet  in  the  form  of  a  straight  bar  is 
usually  called  a  bar  magnet. 

EXPERIMENT   2. 

OBJECT. — To  see  (a)  if  contact  is  necessary  to  get  the 
results  of  Experiment  1,  and  (b)  the  effect  of  interposing 
various  bodies  between  the  magnet  and  the  iron. 

MANIPULATION. — Stand  a  tack  on  its  head  and  bring  the 
magnet  slowly  up  to  it.  Note  particularly  whether  or  not 
the  tack  moves  before  the  magnet  touches  it.  Repeat  the 
experiment,  holding  successively  a  piece  of  paper,  a  piece 
of  glass,  and  a  thin  piece  of  wood  between  the  end  of  the 
magnet  and  the  tack. 

EXPERIMENT   3. 

OBJECT. — To  see  if  the  magnetism  is  of  the  same  strength 
all  along  the  bar;  and  if  not,  how  it  varies  at  different  points. 

MANIPULATION. — Lay  the  magnet  on  a  sheet  of  paper 
and  dust  iron-filings  over  it  all  along  the  bar.  Now  raise 
the  bar.  By  the  number  of  filings  that  adhere  to  the 
various  parts  of  the  magnet  you  can  form  some  idea  of  the 
distribution  of  the  magnetism. 

EXPERIMENT  4. 

OBJECT. — To  see  if  the  distance  between  the  magnet 
and  the  iron  produces  any  effects. 

MANIPULATION. — S^nd  a  large  tack  on  its  head,  slowly 
bring  one  end  of  the  magnet  up  to  it,  and  observe  the 


GENERAL  STUDY  OF  A  MAGNET. 

distance  between  the  end  of  the  tack  and  the  end  of  the 
magnet  when  the  tack  begins  to  mo\7e.  Repeat  with  a 
small  tack. 

EXPERIMENT    5. 

OBJECT.— To  see  what  happens  when  iron  is  brought  be- 
tween the  magnet  and  another  piece  of  iron. 

MANIPULATION— Lay  the  magnet  so  that  one  end  pro- 
jects over  the  edge  of  the  table.  Attach  a  tack  to  it  and 
then  bring  a  second  tack  up  to  the  first.  Try  other  sub- 
stances in  place  of  the  second  tack. 

EXPERIMENT    6. 

OBJECT. — To  measure  the  magnetic  pulls  at  different 
points  of  the  bar. 

MANIPULATION". — Rest  the  centre  of  the  magnet  on  top 
of  a  bottle  or  block  of 
wood,  as  in  Fig.  1,  and 
suspend  a  tack  from  one 
end,  then  carefully  at- 
tach a  second  tack  to 
the  first,  and  so  proceed 
until  you  have  as  long  a 
chain  of  tacks  as  the 
magnet  will  hold.  Count  and  record  the  number  of  tacks. 
Remove  the  chain  and  repeat  from  a  point  about  one-half 
inch  nearer  the  centre  of  the  magnet.  Continue  these 
measurements  at  points  about  one-half  inch  apart  through 
the  length  of  the  magnet.  Make  a  table  of  your  results  as 
follows: 


Distance  from  right-hand  end  of  magnet. 

Number  of  tacks. 

Holding  the  magnet  vertically,  measure   in   the   same 
way  its  power  at  the  ends. 


4  MAGNETISM. 

Definitions. — The  points  in  the  magnet  where  the  mag- 
netism is  the  strongest  are  called  the  Poles. 

When  one  body  moves  towards  another,  as  the  tack 
moved  towards  the  magnet  in  Exercise  1,  it  is  said  to  be 
attracted;  thus,  instead  of  saying  that  the  tack  moved 
towards  the  magnet,  we  would  say  that  the  tack  was  "  at- 
tracted "  by  the  magnet.  Under  the  same  circumstances, 
if  the  body  moved  away,  it  would  be  said  that  it  was 


A  qualitative  experiment  is  one  in  which  whatever  hap- 
pens is  simply  observed;  a  quantitative  experiment  is  one  in 
which  measurements  are  made.  For  example,  Experiment 
6  in  Exercise  1  was  quantitative,  while  all  the  other  experi- 
ments were  qualitative. 

When  a  body  acts  as  if  it  were  pushed  or  pulled,  as  for 
example  the  tack  in  Experiment  1,  it  is  said  to  be  acted 
on  by  &  force. 


EXERCISE  2. 

THE  ACTION  OF  THE  ATTRACTED  BODY  ON  THE  MAGNET. 

Preliminary. — How  the  iron  behaves  toward  a  magnet 
was  shown  in  Exercise  1;  now  it  is  desired  to  find  out 
whether  the  magnet  is  also  affected.  When  the  magnet 
was  brought  up  to  the  tack,  the  tack  moved;  but  the 
magnet,  if  it  tended  to  move,  could  not  do  so  because  it 
was  held  firmly.  In  studying  the  action  of  the  attracted 
body  on  the  magnet,  the  conditions  of  Ex.  1  would  natu- 
rally be  reversed.  The  magnet  would  be  placed  on  the  table 
and  the  tack  held  near  it.  This  could  be  done  if  the  mag- 
net were  very  small,  but  the  magnets  ordinarily  used  are 
so  heavy  that,  if  the  experiment  were  tried  in  that  way,  the 
attraction  would  have  to  be  very  strong  in  order  to  move 
them.  If,  however,  the  magnet  be  suspended,  it  will  not 


ACTION  OF  THE  ATTRACTED  BODY.  5 

rub  against  anything  if  it  tends  to  move,  and  even  a  very 
slight  pull  will  cause  it  to  swing;  therefore  in  the  follow- 
ing Exercise  the  magnet  is  suspended  and  a  body  brought 
up  to  it. 

EXPERIMENT  1. 

Apparatus.— Bar  magnet;  a  new  nail  or  tack;  stirrup  and  thread 
for  suspending  the  magnet.* 

OBJECT. — To  see  if  the  attracted  body  also  attracts  the 
magnet. 

MANIPULATION. — Make  a  small 
stirrup  of  wire  (copper  is  the 
best),  as  in  Fig.  2,  and  by  means 
of  it  suspend  the  magnet  so  that 
it  swings  freely  and  hangs  hori- 
zontally. When  it  has  come  to 
rest,  bring  a  large  nail  near  one 
end,  but  not  touching  it.  Ob- 
serve carefully  what  happens,  and  - 
record. 

Now  repeat  with  the  other  end  of  the  magnet.  Notice 
particularly  whether  the  results  are  the  same  for  both  ends. 

EXPERIMENT  2. 

OBJECT. — To  see  what  happens  when  a  magnet  is  free 
to  move  in  a  horizontal  plane. 

MANIPULATION. — Set  the  suspended  magnet  to  swinging 
gently.  Note  if  it  tends  to  come  to  rest  in  any  particular 
direction,  and  if  so  in  what  direction.  If  there  is  any 
doubt,  after  the  magnet  has  come  to  rest  displace  it  slightly 
and  see  if  it  shows  any  tendency  to  return  to  that  position. 
Does  any  particular  end  of  the  magnet  tend  to  point  in  any 
particular  direction? 

*  If  a  compass  is  available,  it  may  be  conveniently  substituted 
for  the  suspended  magnet. 


6  MAGNETISM. 

Definitions. — If  something  happens  to  one  substance 
when  another  substance  is  brought  near  it,  the  second  is 
said  to  act  on  the  first.  If  the  action  is  mutual,  either 
body  may  be  said  to  act  and  the  other  would  then  be  said 
to  react.  Does  a  magnet  act  on  a  piece  of  iron  ?  Is  there 
any  reaction  ?  If  so,  where  ? 

The  pole  of  a  magnet  that  tends  to  point  north  is  called 
the  North-seeking  or  North  pole.  In  the  same  way  the 
other  is  called  the  South  pole. 

When  new  properties  are  developed  in  one  body  by  bring- 
ing another  body  near  it,  the  new  properties  of  the  first 
body  are  said  to  be  induced  by  the  second. 

Any  contrivance  for  getting  desired  conditions  is  called 
a  piece  of  apparatus;  for  instance,  a  compass  is  a  contrivance 
or  piece  of  apparatus  for  arranging  a  magnet  so  that  it  can 
swing  freely. 

When  the  same  experiment  has  beeniried  a  great  many 
times,  with  the  same  results  wherever  or  whenever  it  was 
tried,  such  results  are  said  to  be  a  law.  For  example, 
whenever  a  magnet  has  been  brought  near  a  piece  of  iron 
that  could  move,  the  iron  has  moved  towards  the  magnet; 
and  whenever  the  magnet  has  been  placed  under  such  con- 
tions  that  it  could  move,  it  has  moved  toward  the  iron. 
Whenever  this  has  not  happened,  it  has  always  been  found 
that  some  other  conditions  had  been  introduced  into  the 
experiment,  and  when  these  were  removed  the  usual 
results  have  taken  place;  hence  it  is  said  to  be  a  law  that  a 
magnet  attracts  a  piece  of  iron  and  the  piece  of  iron  at- 
tracts the  magnet. 

EXERCISE  3. 

MUTUAL  ACTION  OF  TWO  MAGNETS. 

Preliminary.— So  far,  magnets  have  been  studied;  but 
in  the  following  Exercise  the  subjects  are  not  magnets,  but 
magnetic  poles,  and  it  is  desired  to  study  the  action  of  one 


MUTUAL  ACTION  OF  TWO  MAGNETS.  7 

magnetic  pole  on  another.  In  order  to  do  this,  one  pole 
must  be  free  to  move  and  the  other  must  be  brought  near 
it.  As  there  are  two  kinds  of  poles,  both  like  and  unlike 
poles  must  be  tried.  It  is  impossible  to  get  the  poles  alone, 
so  whole  magnets  must  be  used;  and  in  order  to  have  the 
poles  free  to  move,  one  magnet  must  be  suspended.  The 
same  device  could  be  used  as  in  Exercise  2,  but  a  more 
convenient  apparatus  is  a  compass,  which  consists  of  a 
magnet  supported  on  a  sharp  point  and  contained  in  a 
circular  box,  usually  provided  with  a  glass  cover. 

EXPERIMENT  1. 

Apparatus.— Bar  magnet;  compass;  wood;  glass;  paper;  etc.  (as 
in  Ex.  1). 

OBJECT. — To  study  what  takes  place  when  two  magnetic 
poles  are  brought  near  each  other,  one  pole  being  free  to 
move. 

MANIPULATION. — Take  a  compass  and  find  the  north 
pole  (Ex.  2,  Exp.  2).  Lay  the  bar  magnet  on  the  table 
and  bring  the  north  pole  of  the  compass-needle  up  to  the 
north  pole  of  the  magnet.  In  the  same  way  try  bringing 
the  north  pole  of  the  compass-needle  up  to  the  south  pole 
of  the  magnet.  Try  also  the  south  pole  of  the  compass  and 
the  south  pole  of  the  magnet,  and  the  south  pole  of  the 
compass  and  the  north  pole  of  the  magnet.  Tabulate  your 
results  as  follows : 


Pole  of  Compass. 

Pole  of  Magnet. 

Results. 

From  the  study  of  the  table,  write  in  your  note-book  the 
"  law"  of  the  action  of  magnetic  poles. 

EXPERIMENT  2.. 

OBJECT.— To  see  if  the  results  of  Experiment  1  still  hold 
when  various  bodies  are  placed  between  the  poles, 


8 


MAGNETISM. 


MANIPULATION. — Repeat  Experiment  1  with  pieces  of 
wood,  glass,  paper,  etc.,  held  between  the  poles.  Tabulate 
results  as  follows : 


1st  Pole. 

2d  Pole. 

Body  Used. 

Results. 

EXERCISE  4. 

INDUCED   MAGNETISM.      BREAKING   MAGNETS. 
EXPERIMENT  1. 

Apparatus.— Bar  magnet;  compass;  large  darning-  or  knitting, 
needle  of  quite  hard  steel;  piece  of  iron  wire;  copper  wire  (say  No. 
16);  large  horse-shoe  nail ;  iron-filings;  piece  of  paper  on  which  to 
put  the  filings;  pieces  of  wood,  and  glass  rod  or  tubing. 

OBJECT. — To  observe  the  effect  of  bringing  a  piece  of 

steel  in  contact  with  a  magnet. 

MANIPULATION. — Take  a  large  darning-needle  and  stroke 

one  end,  always  in  the  same  direction,  several  times  on  one 
pole  of  a  bar  magnet,  is  shown 
in  Fig.  3.  Note  the  nature  of  the 
pole  used.  Bring  the  end  of  Hie 
needle  that  you  stroked  on  the  mag- 
net up  to  a  compass-needle.  Note 
what  change  has  been  produced  in 
the  darning-needle.  Test  the 

other  end  in  the  same  way 

EXPERIMENT  2. 

OBJECT.— To  find  out  how  the  nature  of  the  inducing 
pole  affects  the  nature  of  the  induced  pole. 

MANIPULATION. — Compare  the  nature  of  the  pole  in- 
duced in  the  end  of  the  needle  that  was  rubbed  on  the 
magnet  with  the  nature  of  the  pole  on  which  it  was  rubbed. 
Test  the  nature  of  the  poles  by  the  knowledge  gained  in 
Ex.  3.  Test  also  the  other  end  of  the  needle.  State  in 
your  note-book  the  law  for  the  induction  of  magnetic  poles, 


FIG.  3. 


INDUCED  MAGNETISM.     BREAKING  MAGNETS.       9 
EXPERIMENT  3. 

OBJECT. — To  see  if  all  substances  can  be  magnetized. 

MANIPULATION. — Repeat  Exp.  I  with  the  following: 
Soft  iron  wire  which  you  are  sure  is  not  magnetized,  wood, 
glass,  and  copper.  Tabulate  your  results. 

EXPERIMENT  4. 

OBJECT. — To  observe  the  results  of  breaking  a  magnet. 

MANIPULATION. — Break  your  magnetized  needle  in  the 
centre  and,  with  the  compass,  examine  both  ends  of  each 
part.  Record  results,  and  draw  figures  illustrating  them. 

EXPERIMENT  5. 

OBJECT. — To  find  what  happens  when  the  broken  parts 
of  the  magnet  are  put  together  again. 

MANIPULATION. — Bring  the  broken  parts  of  Exp.  4 
together,  opposite  poles  in  contact,  and  with  the  compass 
examine  it  all  along  its  length  for  magnetism.  From  these 
results  suggest,  if  you  can,  why  the  centre  of  a  magnet  shows 
no  magnetism.  Break  one  half  of  your  needle  and  test  each 
half  as  before.  As  the  magnet  is  broken  into  smaller  and 
smaller  pieces,  what  will  apparently  be  true  of  each  part  ? 

EXPERIMENT  6. 

OBJECT. — To  see  if  a  change  is  produced  in  a  piece  of 
iron  when  brought  near  a  pole.  (Compare  this  with 
Exercises  1  and  2.) 

MANIPULATION. — Take  a  wrought-iron  horseshoe-nail, 
test  it  to  make  sure  that  it  is 
free  from  magnetism,  and  then 
hold  it  vertically  with  the  lower 
end  in  some  iron-fillings;  bring 
the  magnet  over  the  upper  end 
of  the  nail,  but  not  in  contact  1  [ 

with  it.  (See  Fig.  4.)  Lift  the 
magnet  and  nail  together,  still 
holding  them  a  little  distance  FIG.  4. 

apart.     Observe  results,    Take  away  the  magnet  and  again 


10  MAGNETISM. 

observe  results.  Repeat  the  experiment  with  the  other 
pole  of  the  magnet.  Try  putting  a  piece  of  paper  between 
the  magnet  and  the  nail.  Put  the  bar  magnet  entirely  out 
of  the  way  and  test  the  nail  for  magnetism  by  means  of  the 
compass.  After  a  lapse  of  five  or  ten  minutes  test  the  nail 
again. 

State  in  your  notes  anything  that  you  have  observed 
regarding  the  different  behavior  of  iron  and  steel  when 
brought  near  or  in  contact  with  a  magnet.  If  needed, 
Exp.  6  may  be  repeated  roughly,  with  the  nail  and  the 
magnet  in  contact. 

QuESTiONSo — What  tests  could  you  apply  to  distinguish 
a  magnet  from  a  piece  of  steel  ?  Why  are  magnets  made 
of  steel  instead  of  iron  ? 

EXERCISE  5. 

LAW  OF  INDUCED  MAGNETS. 

Preliminary. — When  a  piece  of  iron  or  steel  is  mag- 
netized by  being  brought  near  or  in  contact  with  a  magnet, 
it  is  said  to  be  an  induced  magnet,  and  the  original  magnet 
is  said  to  be  an  inducing  magnet. 

The  different  behavior  of  iron  and  steel  is  expressed  by 
saying  that  the  steel  has  a  greater  retentivity  than  iron. 

The  magnetism  remaining  in  a  piece  of  soft  iron  after 
the  inducing  magnet  has  been  removed  is  called  residual 
magnetism. 

In  the  following  exercise,  we  wish  to  find  out  how  the 
poles  of  the  inducing  magnet  affect  the  poles  of  the  in- 
duced magnet. 

EXPERIMENT    1. 

Apparatus.— Bar  magnet;  compass;  2  horseshoe-nails,  or  2  pieces 
of  soft  iron  wire,  3  or  4  inches  long.  If  nails  are  used,  they  will  prob- 
ably have  to  be  new  ones,  as  the  nail  used  in  Exercise  4  will  probably 
retain  some  magnetism. 

OBJECT, — To  study  the  nature  of  the  pole  of  the  induced 


LAW  OF  INDUCED  MAGNETS. 


11 


magnet,  furthest  from  the  inducing  pole. 

MANIPULATION". — Arrange  apparatus  as  in  Fig.  5,  where 
AB  represents  the  bar  magnet,  CD  represents  a  soft  iron 


FIG.  5. 

nail  (free  from  all  magnetism),  and  N8  represents  the 
compass.  Be  sure  that  the  direction  in  which  the  nail  and 
magnet  lie  is  an  east  and  west  one,  i.e.,  at  right  angles  to 
the  normal  position  of  the  compass-needle.  Starting  with 
the  magnet  three  or  four  inches  from  the  end  of  the  nail, 
slowly  bring  it  up  to  the  end  0.  Note  how  the  end  D 
affects  the  north  pole  of  the  compass-needle.  Eepeat, 
using  the  south  pole  of  the  magnet.  State  in  your  notes 
how  you  find  the  pole  of  the  induced  magnet  at  the  end 
furthest  from  the  pole  of  the  inducing  magnet  to  compare 
with  the  inducing  pole  of  the  inducing  magnet.  Illustrate 
by  a  diagram. 

EXPERIMENT  2. 

OBJECT. — To  discover  the  nature  of  the  induced  pole 
nearest  to  the  inducing  pole. 


FIG.  6. 


MANIPULATION. — Arrange  apparatus  as  in  Fig.  6. 

The  distance  from  the  pole  of  the  magnet  to  the  pole  of 


12  MAGNETISM. 

the  compass-needle  should  be  about  an  inch.  When  the 
nail  is  brought  close  to  the  pole,  it  becomes  an  induced 
magnet  and,  if  suddenly  removed  from  the  pole,  retains  its 
magnetism  for  an  instant.  (See  Ex.  4,  Exp.  6.)  When  the 
compass-needle  is  at  rest,  suddenly  move  the  end  of  the  nail 
which  is  in  front  of  the  magnetic  pole  up  to  the  compass. 
The  induced  pole  in  the  nail,  remaining  for  an  instant,  is 
brought  so  much  nearer  to  the  pole  of  the  compass  that 
its  action  is  noticeable,  in  spite  of  the  greater  action  of  the 
pole  of  the  bar  magnet.* 

EXERCISE  6. 

LINES  OF  MAGNETIC  FORCE. 

Preliminary. — We  know  from  previous  experiments  that 
the  space  around  the  poles  of  a  magnet  is  in 
such  a  condition  that  a  body  which  can  be 
magnetized  is  acted  upon  when  brought  into 
that  space.  This  space  is  called  the  field  of  a 
magnet.  If  the  body  moves  towards  the  magnet, 
it  moves  in  the  direction  of  the  force,  that  is,  in 
the  direction  in  which  the  magnetic  push  or 
pull  is  exerted.  Suppose  a  small  piece  of  iron 
placed  near  a  magnetic  pole,  as  in  Fig.  7.  It  is 
magnetized  by  induction  and  becomes  a  magnet. 
The  end  nearest  the  inducing  magnet  will  be, 
as  shown  in  the  figure,  a  pole  opposite  to  the 
FIG.  7.  nearest  pole  of  the  inducing  magnet.  The  pole 
farthest  from  the  inducing  pole  will  be  like  it.  The  bit 
of  iron  will  be  attracted  at  one  end  and  repelled  at  the 
other  end  with  practically  equal  force,  hence  it  will  not 
tend  to  move  toward  the  magnet,  but  will  swing  around 
until  its  length  lies  in  the  line  of  the  push  and  pull. 

To  illustrate  this,  imagine  a  stick  lying  on  the  floor, 

*  SUGGESTION. — Prepare  an  essay  on  Induced  Magnetism. 


LINES  OF  MAGNETIC  FORCE.  13 

with  a  string  attached  to  each  end,    as  in  Fig.  8.     On 
pulling  both  strings  the  stick   will  not  move  in  either 


FIG.  8. 

direction,  but  will  twist  around  on  its  centre  until  it  lies 
in  the  line  in  which  the  strings  were  pulled,  as  in  the 
second  diagram. 

The  lines  marking  the  direction  of  the  magnetic  push 
or  pull  are  called  lines  of  magnetic  force.  In  the  follow- 
ing exercise  we  wish  to  observe  these  lines  for  various  cases. 

EXPERIMENT. 

Apparatus.— A  piece  of   sized    writing-paper;    fine  iron-filings; 
two  bar  magnets;  shellac;  glass  tube;  blocks  of  wood. 

OBJECT. — To  study  the  lines  of  magnetic  force. 

MANIPULATION. — Take  a  piece  of  glazed  paper,  and 
pour  fine  iron-filings  on  it.  Pour  off  the  iron-filings  and 
you  will  find  that  a  layer  of  iron-dust  remains  on  the  paper. 
Lay  a  bar  magnet  on  the  table,  hold  the  paper  horizontally 
over  it  and  then  bring  it  straight  down  until  it  rests  upon 
the  magnet.  If  the  magnet  can  be  placed  between  two 
blocks  of  wood  whose  thickness  is  the  same  as  the  depth 
of  the  bar,  so  that  the  paper  lies  on  a  level  surface,  better 
results  can  be  obtained.  Tap  the  paper  very  gently  with 
a  lead-pencil  and  the  little  particles  of  iron  will  swing 
around  on  their  centres  until  they  everywhere  lie  in  the 
line  of  the  magnetic  force.  There  will  also  be  a  number  of 


14  MAGNETISM. 

lines  on  the  paper  which  surround  the  outline  of  the  mag- 
net. These  lines  are  called  lines  of  force,  and  each  line 
represents  the  line  of  the  magnetic  force  in  its  part  of  the 
field.  If  a  good  set  of  lines  is  not  obtained  with  one  or  two 
gentle  taps,  remove  the  paper  and  try  again,  as  continual 
tapping  will  only  cause  the  iron  particles  to  bunch. 

The  positions  taken  by  the  iron-filings  now  give  the 
diagram  of  the  lines  of  force,  and  in  order  to  study  them 
they  must  be  preserved  in  some  way. 

Method  1.  Lift  the  paper  vertically  off  the  magnet  to  a 
height  of  about  6  inches,  then  gently  place  it  on  the  table 
and  carefully  copy  on  another  piece  of  paper  the  diagram 
obtained. 

Method  2.  With  a  lead-pencil  trace  out  the  different  lines 
one  after  another  on  the  paper  itself.  On  wiping  off  the  iron- 
dust  you  will  have  a  fairly  good  reproduction  of  the  lines. 
Method  3.  If  it  is  desired  to  preserve  in  place  the  parti- 
cles of  iron  themselves,  there  will  be  needed,  in  addition 
to  the  other  apparatus,  some  thin  shellac  and  a  glass  tube, 
open  at  both  ends,  about  £  in.  internal  diameter  and  3  in. 
long.  Holding  this  tube  as  in  Fig.  9,  insert  one  end  into 
the  shellac  and  remove  the  finger  from  the  top  for  an 
instant.  Keplace  the  finger  and  lift  the  tube  from  the 
liquid.  So  long  as  the  finger  is  pressed  on  the  «top  of  the 
tube  some  shellac  will  remain  inside  and  may  be  allowed 
to  run  out  by  raising  the  finger.  With  the  paper  lying 
upon  the  magnet,  rest  the  tube  very  gently  on  the  paper 

just  inside  the  outline  of  the 
magnet  (at  the  point  marked 
x  in  Fig.  9),  inclining  it 
at  an  angle  of  about  45°. 
After  it  is  on  the  paper, 
but  not  before,  remove  the 
Fl°-  9-  finger,  thus  allowing  the 

shellac  to  run  out.     The  rate  at  which  the  shellac  flows 


LINES  OF  MAGNETIC  FORCfl.  1 

may  be  regulated  by  the  degree  to  which  the  finger  is 
removed.  Care  must  be  used  to  prevent  the  shellac  from 
running  out  with  sufficient  force  to  move  the  iron  parti- 
cles. If  the  operation  is  properly  conducted,,  the  particles 
will  not  be  disturbed  and  the  shellac  will  soak  in  among 
them.  If  the  first  application  of  shellac  does  not  en- 
tirely cover  the  figure,  more  may  be  added,  with  the  same 
precaution,  at  other  parts  of  the  paper.  The  greatest 
care  must  be  used  not  to  allow  any  of  the  liquid  to  drop  on 
the  paper,  as  it  will  displace  the  iron-dust  where  it  strikes. 
When  the  operation  is  completed,  it  is  best  to  leave  the 
paper  until  the  alcohol  has  evaporated,  which  may  be  in 
five  or  ten  minutes.  During  this  time  be  careful  that  the 
paper  is  not  disturbed.  If  in  a  hurry,  the  paper  may  be 
lifted  vertically  from  the  magnet  and  placed  upon  a  hori- 
zontal surface  until  dry.  When  the  shellac  has  become 
hard  the  iron  is  permanently  fixed  and  the  figure  may  be 
pasted  in  the  note-book. 

Method  4.  For  this  the  shellac  should  be  somewhat 
thicker  than  in  the  preceding  method.  Place  the  paper 
over  the  magnet  and  pour  the  shellac  on  the  paper,  allow- 
ing it  to  spread  out  in  a  thin  layer.  Then  carefully  scatter 
the  iron-dust  over  it  and  the  iron  particles  will  spread 
in  the  shellac,  on  which  they  will  float.  Tap  gently  until 
the  lines  appear,  and  allow  the  paper  to  remain  undisturbed 
until  dry. 

By  one  of  these  methods  obtain  the  lines  of  force  in  the 
following  cases:  1.  A  north  pole.  2.  A  south  pole. 
3.  Two  like  poles.  (Use  two  bar  magnets  end  to  end,  the 
ends  being  about  half  an  inch  apart.)  4.  Two  unlike 
poles,  arranged  in  the  same  way  as  in  3. 

QUESTIONS. — 1.  What  is  the  form  of  the  lines  of  force 
around  a  single  magnetic  pole  ?  2.  What  is  the  shape 
of  the  lines  of  force  around  two  like  poles  situated  near 
each  other?  3.  What  is  the  shape  of  the  lines  of  force 


16  MAMETI8M. 

around  two  uulike  poles  situated  near  each  other?  4. 
How  does  the  form  of  the  lines  of  force  around  two  like 
poles  compare  with  the  form  of  the  lines  of  force  around 
two  unlike  poles  ?  5.  In  what  case  are  the  lines  continu- 
ous from  pole  to  pole,  and  in  what  case  are  they  not  ? 
6.  How  do  the  lines  of  force  compare  around  a  north  or 
south  pole  when  no  other  poles  are  near  ? 


CURBENT  ELECTRICITY. 
EXERCISE  1. 

VOLTAIC    ELECTRICITY. 

Introductory. — The  word  Electricity  is  the  name  given 
to  the  cause  of  certain  phenomena,  just  as  Magnetism  is 
the  name  given  to  the  cause  of  certain  other  phenomena, 
such  as  the  attraction  of  iron  and  steel  by  a  magnet  or  the 
attraction  and  repulsion  of  magnetic  poles; 

When  chemical,  as  well  as  some  other  changes  are  pro- 
duced under  certain  conditions,  the  resulting  phenomena 
are  said  to  be  caused  by  electricity.  When  these  phenom- 
ena are  produced  by  chemical  change,  they  are  said  to  be 
due  to  current  or  voltaic  electricity.  In  the  following 
exercises  some  of  these  phenomena  are  observed,  the  con- 
ditions under  which  they  can  be  brought  about  in- 
vestigated, and  some  points  connected  with  the  useful 
applications  of  electricity  examined. 

EXPERIMENT  1. 

Apparatus.— 5  test-tubes  ;  a  bit  of  zinc  ;  a  copper  tack  ;  an  iron 
nail ;  a  piece  of  carbon  (electric-light  carbon  or  piece  of  old  battery 
carbon);  a  piece  of  amalgamated  sheet  zinc;  copper  and  zinc  strips; 
diluted  sulphuric  acid  ;  compass  ;  tumbler ;  some  means  of  sup- 
porting the  tubes  in  an  upright  position;  bar  magnet. 

OBJECT. — To  observe  the  action  of  dilute  sulphuric  acid 
on  a  number  of  substances.* 

MANIPULATION". — Take  5  test-tubes  and  in  each  place 
5  cc.  10$  f  sulphuric  acid.  Place  in  each  tube  one  of 

*  Much  time  can  be  saved  by  working   this  experiment  simul- 
taneously with  Experiment  2. 
f  One  part  of  strong  acid  to  nine  parts  of  water. 

17 


18  tiVRRENT  BLECTRlGITY. 

the  following  substances:  zinc,  copper,  iron,  carbon,  and 
a  bit  of  zinc  which  has  first  been  wet  with  acid  and  then 
rubbed  with  mercury.*  From,  time  to  time  during  15  or 
20  minutes,  watch  carefully  what  goes  on  and  record  your 
observations.  Watch  particularly  for  answers  to  the  fol- 
lowing questions,  but  make  in  addition  a  complete  record 
of  all  that  takes  place. 

QUESTIONS. — 1.  Does  any  change  go  on  ?  2.  If  so,  is  it 
the  same  in  all  the  tubes  ?  3.  Has  there  been  any  change 
in  the  size  of  the  bodies  ?  4.  Arrange  the  names  of  the 
bodies  in  the  order  of  the  energy  of  the  action,  beginning 
with  the  body  acted  on  the  least  and  ending  with  that 
acted  on  the  most.f  5.  In  any  of  the  tubes  is  there  any 
change  in  the  nature  of  the  action  after  it  has  gone  on  for 
a  while  ?  If  such  a  case  is  noted,  make  a  careful  record  of 
all  that  is  observed  in  connection  with  it.  6.  Summarize 
what  has  been  learned  regarding  the  action  of  cold  dilute 
sulphuric  acid  on  various  substances. 

EXPERIMENT    2. 

Apparatus.— Strip  of  copper,  strip  of  zinc  (unamalgamated),  with 
wires;  a  tumbler;  dilute  sulphuric  acid ;  compass. 

OBJECT. — To  observe  how  electric  phenomena  may  be 
brought  about  by  chemical  action. 

MANIPULATION'. — You  are  provided  with  two  strips,  one 
of  copper  and  one  of  zinc,  a  copper  wire  being  attached  to 
each.  Place  these  strips  in  the  tumbler  and  pour  in  10$ 
sulphuric  acid  until  the  plates  are  covered  to  a  depth  of 
about  two  inches.  The  acid  must  not  be  deep  enough  to 
cover  the  points  where  the  wires  are  attached  to  the  plates. 

*  Zinc  so  treated  is  said  to  be  amalgamated. 

f  The  bubbles  of  air  which  may  slowly  come  out  of  some  of  the 
bodies,  particularly  the  carbon,  are  not  to  be  confounded  with  the 
bubbles  of  hydrogen  gas  given  by  the  chemical  action.  The  air  has 
no  smell,  the  hydrogen  has.  On  thrusting  a  lighted  match  into 
hydrogen  the  gas  will  usually  burn. 


VOLTAIC  ELECTRICITY. 


19 


FIG.  10. 


During  this  operation,  do  not  allow  the  strips  to  come  in 
contact.  To  prevent  this,  before  pouring  in  the  acid 
arrange  as  in  Fig.  10,  bending  the  wires  back  so  as  to 
spring  against  the  sides, 
thus  holding  the  two  plates 
on  opposite  sides  of  the 
tumbler.  Note  carefully 
what  happens  on  each 
plate,  then  bring  the  wires 
in  contact,  watching  each 
plate  carefully  while  you 
do  so.  Lay  the  compass  on 
the  table  and  arrange  ap- 
paratus as  in  Fig.  11,  so  that  when  the  compass-needle  is 
at  rest,  one  of  the  wires  lies  directly  beneath  and  parallel  to 

it.  While  arranging  this, 
the  wires  must  not  be  in 
contact.  Now  connect  the 
ends  of  the  wires.*  What 
goes  on  in  the  tumbler? 
What  goes  on  in  the  com- 
FIG-  "'  pass  ?  Disconnect  the 

wires  and,  when  the  compass-needle  has  come  to  rest,  hold 
a  bar  magnet  about  six  inches  above  it.  Bring  the  magnet 
slowly  down  to  the  compass,  watching  the  needle  as  you  do 
so.  Find  in  what  direction  the 
magnet  must  be  held,  and  how 
it  must  be  moved  to  produce  the 
same  effect  on  the  compass- 
needle  that  was  produced  by  (1) 
connecting  the  wires,  (2)  discon- 
necting them.  How  could  a 
number  of  magnets  be  arranged  so  as  to  produce  the  same 

*  Should  any  marked  phenomena  fail  to  appear  on  bringing  the 
wires  in  contact,  remove  plates,  clean  carefully,  and  repeat. 


^      3- 


FIG.  12. 


20  CURRENT  ELECTRICITY. 

effect  on  the  compass  as  was  produced  by  the  wires  ?    Il- 
lustrate by  a  sketch  in  your  note-book. 


EXERCISE   2. 

CONDITIONS   FOR    PRODUCING    CURRENT. 

Preliminary. — When,  on  bringing  a  wire  near  a  compass- 
needle,  or  any  magnet  free  to  deflect,  a  phenomenon  like 
that  in  the  preceding  exercise  is  observed,  the  wire  is  said 
to  have  a  current  of  electricity  flowing  through  it.  We 
do  not  know  exactly  what  goes  on  in  the  wire,  or  why 
the  needle  acts  as  it  does;  and  when  we  say  that  a  wire 
is  carrying  a  "current "we  only  mean  that,  if  the  wire 
were  brought  near  a  compass-needle,  the  needle  would  be 
affected  as  we  have  observed  in  the  preceding  exercise. 
The  wire  is  the  same  wire  whether  it  "carries  a  current" 
or  not.  When,  for  example,  one  plate  is  lifted  from  the 
liquid,  the  power  of  the  wire  to  twist  the  needle  dis- 
appears. This  also  happens  if  the  wire  is  not  complete 
from  one  plate  to  another.  But  while  we  do  not  change 
the  wire,  we  do  change  the  conditions  under  which  the 
wire  is  placed.  Hence  when  we  speak  of  a  wire  carrying  a 
current  we  imply  a  special  condition  of  the  wire.  The  steps 
necessary  to  develop  in  a  wire  the  power  indicated  by  the 
compass-needle  are  called  the  conditions  needed  for  the  pro- 
duction of  an  electric  current.  As  will  be  seen  later,  there 
are  other  ways  in  which  this  condition  of  the  wire  may  be 
brought  about  besides  that  of  the  galvanic  cell ;  but  no 
matter  what  has  been  done  to  a  wire,  if  it  can  do  what  the 
Wire  in  the  preceding  exercise  could  do,  it  is  said  to  carry  a 
current  while  in  that  condition,  and  at  no  other  time. 

QUESTIONS. — Define  electricity;  an  electric  current.  How 
could  you  determine  whether  a  telegraph-wire  was  carrying 
a  current  or  not  •>  Name  any  method  for  generating  elec- 


CONDITIONS  FOR  PRODUCING  CURRENT.          21 

tricity  besides  the  chemical  one.  Must  anything  be  de- 
stroyed in  order  that  the  current  may  be  generated  ? 

Diagrams. — Figs.  11  and  12  1fl5th  represent  the  set  of 
apparatus  used  in  this  exercise.  On  examining  them, 
however,  you  will  see  that  Fig.  11  is  a  picture  of  the  ap- 
paratus, showing  it  as  it  actually  looks,  while  Fig.  12  bears 
no  resemblance  to  it  at  all.  In  Fig.  12  the  tumbler  and 
plates  are  represented  by  a  circle  with  two  lines  inside,  the 
compass  by  a  circle  with  a  long  diamond  inside,  and  the 
wires  by  lines.  It  is  not  necessary  to  show  what  the 
tumbler  looks  like,  or  what  the  compass  looks  like,  or  what 
sort  of  wires  are  used;  the  essential  thing  is  to  make  clear 
that  the  wire  connecting  the  plates  is  carried  under  the 
compass  in  a  north  and  south  line,  and  this  is  done  just 
as  well  in  Fig.  12  as  in  Fig.  11.  Such  a  figure  as  Fig.  12, 
which  only  shows  the  way  in  which  the  parts  of  the  appa- 
ratus are  arranged  to  bring  about  the  conditions  under 
which  the  experiment  is  worked,  is  called  a  diagram;  and  as 
diagrams  are  much  easier  to  draw,  in  scientific  work  they 
are  often  used  in  place  of  pictures. 

In  making  diagrams,  each  instrument  has  its  own  sign. 
Where  a  picture  of  an  instrument  is  given  in  this  book, 
the  sign  by  which  it  is  to  be  represented  in  diagrams  is 
also  given  (for  example,  see  Figs.  13  and  14).  Unless 
otherwise  instructed,  always  represent  apparatus  by  dia- 
grams in  your  note-book,  and  the  instruments  by  the 
regular  signs.  Use  a  ruler  whenever  you  can,  and  be  care- 
ful to  make  the  diagram  large  enough.  A  space  at  least 
3x3  inches,  and  often  even  half  a  page  or  a  whole  page  of 
your  note-book  should  be  used.  A  space  reserved  for  a 
diagram  should  never  have  notes  written  in  it.  In  a  dia- 
gram the  different  parts  are  usually  indicated  by  letters, 
generally  the  initials  of  the  names  of  those  parts ;  thus  a 
compass  is  marked  C,  a  wire  W,  etc.  Where  the  same 
letters  have  to  be  used  more  than  once,  one  or  more  accents 


22  CURRENT  ELECTRICITY. 

are  added.  For  example,  if  two  wires  were  to  be  marked, 
they  would  be  lettered  W  and  W  (W prime),  respectively, 
and  a  third  wire  would  be  marked  W"  (W  second).  Or 
capitals  and  small  letters  might  be  used. 


EXPERIMENT    1. 

Apparatus.— Copper  strip  ;  zinc  of  "tumbler  cell"  (amalga- 
mated); tumbler  ;  compass  ;  dilute  acid  ;  iron  plate  ;  carbon  plate 
of  cell;  water;  nail;  wood;  glass;  etc. 

OBJECT. — (a)  To  observe  the  effects,  in  the  tumbler  and 
on  the  compass-needle,  of  amalgamating  the  zinc,  (b)  To 
study  the  conditions  under  which  this  effect  on  the  com- 
pass-needle can  be  produced. 

MANIPULATION. — Part  1.  Proceed  as  in  the  preceding 
exercise,  noting  carefully  what  goes  on  in  the  tumbler  with 
amalgamated  zinc,  the  wires  first  in  contact,  then  not  in 
contact.  Eepeat  the  test  with  the'  wire  and  compass. 

QUESTIONS. — What  effect  has  the  amalgamation  of  the 
zinc  on  (1)  the  action  in  the  tumbler  when  the  wires  are 
not  in  contact  ?  (2)  the  action  in  the  tumbler  when  the 
wires  are  in  contact?  (3)  the  action  of  the  wire  on  the 
compass-needle  ? 

Part  II.  (a)  Bring  the  wires  in  contact  and,  holding 
one  wire  over  the  compass,  cause  the  needle  to  deflect. 
Still  holding  the  wire  over  the  compass,  separate  the  ends 
(it  is  well  to  tap  the  compass  gently,  as  the  needle  is 
liable  to  stick).  Having  again  caused  the  needle  to  deflect, 
raise  one  plate  from  the  liquid.  Note  what  happens  in 
the  compass  and  in  the  tumbler.  Replace  the  plate,  watch- 
ing carefully  for  any  changes.  Try  the  other  plate,  (b) 
As  regards  the  nature  of  the  liquid:  replace  the  acid  in 
the  tumbler  by  water,  trying  the  compass  test  and  watch- 
ing the  tumbler  carefully,  (c)  As  regards  the  relation  of 
the  plates  to  the  liquid  :  place  in  the  acid  two  strips  of 


CONDITIONS  FOR  PRODUCING  CURRENT.          23 

zinc,  also  try  two  strips  of  copper.*  Repeat  the  compass- 
test.  Try  other  metals — zinc  and  iron,  zinc  and  carbon, 
iron  and  carbon.  In  each  case  try  the  compass-test  and 
watch  carefully  what  goes  on  in  the  tumbler. 

QUESTIONS. — 1.  Can  the  compass-needle  effect  be  pro- 
duced with  any  two  plates  ?  2.  Do  the  plates  all  produce 
the  same  effect  ?  If  not,  name  them  in  the  order  of  the 
amount  of  deflection  they  produce.  3.  Is  any  change  notice- 
able in. the  plates  as  the  action  goes  on?  If  so,  where? 
4.  Can  the  plates  be  connected  by  any  substance  ?  Lay  a 
nail  over  the  compass  and  touch  the  ends  of  the  wires  one 
to  each  end.  Try  in  the  same  way  wood,  glass,  wire,  etc. 
Note  the  behavior  of  the  compass  in  each  case.  (5)  What 
conditions,  then,  must  be  fulfilled  in  order  that  the  mag- 
netic needle  shall  be  deflected  by  the  wire  as  regards  (a) 
the  wire,  (b)  the  plates,  (c)  the  liquid,  (d)  the  magnetic 
needle  ? 

Supplementary.— An  arrangement  of  plates,  liquid,  etc., 
fulfilling  the  conditions  found  in  the  this  exercise,  is  called 


FIG.  13. 


a  galvanic  cell.    The  plates  are  called  the  elements  or 
plates.      The  fluid    is  called    the    exciting  fluid.      The 

*  Exchange  strips  with  your  neighbor. 


CURRENT  ELECTRICITY. 


wires  leading  from  the  plates  are  called  the  conductors,  or 
the  leading  wires.  One  form  of  cell  is  shown  in  Fig.  13. 
The  plates  of  carbon  (C)  and  zinc  (Z)  are  separated  by 
pieces  of  wood  ( WW)  and  held  in  place  by  a  rubber  band 
(RR).  The  plates  are  set  in  a  glass  vessel  to  contain  the 
exciting  liquid,  and  to  each  plate  is  attached  a  wire,  as 
shown  in  the  figure.  In  diagrams  a  cell  is  usually  indi- 
cated by  two  parallel  lines  of  unequal  length,  as  B  in  Fig. 


-j- 


FIG.  14. 


14,  which  would  represent 
one  cell.  The  connecting 
wires  are  indicated  by  straight 
lines,  as  shown,  while  arrows 
near  the  lines  indicate  the 
direction  of  the  current. 
When  the  cell  is  so  arranged 
that  the  current  is  passing 
through  the  conductors,  as  in 
Fig.  14,  the  cell  is  sometimes 
said  to  be  running.  Although 
we  only  know  that  the  wires 
possess  certain  properties  when  the  cell  is  running  that 
they  do  not  possess  when  the  cell  is  not  running,  it  has 
been  customary  to  imagine  that  electricity  flows  through 
the  wire,  and  to  speak  of  a  current  of  electricity  We  have 
no  means  of  finding  out  which  way  this  current  flows, 
but  it  is  generally  considered  as  flowing  in  the  wire  con- 
necting the  plates  from  the  metal  least  acted  upon  to  that 
most  acted  upon,  and  through  the  liquid  in  the  cell  in  the 
reverse  direction.  The  plate  from  which  the  current  is  sup- 
posed to  flow  in  the  wires  is  called  the  positive  plate,  and  is 
indicated  by  the  -\-  sign.  The  plate  to  which  the  current 
flows  is  called  the  negative  or  minus  plate,  and  is  indicated 
by  the  —  sign.  The  whole  path  of  the  current,  plates, 
liquid,  and  conductors  is  called  the  circuit. 


ACTION  OF  CURRENTS  ON  MAGNETS. 


EXERCISE    3. 

ACTION    OF    CURRENTS    ON   MAGNETS. 

EXPERIMENT   1. 

Apparatus.— About  100  cm.  of  No.  18  insulated  copper  wire  ;  com- 
pass ;  electric  current.    Tumbler-cell.    Supports  for  compass. 

OBJECT. — To  study  the  conditions  affecting  the  behavior 
of  a  magnetic  needle  free  to  move,  when  near  an  electric 
current. 

MANIPULATION. — 1.  Place  the  wire  over  the  needle  in  a 
north  and  south  line,  arranging  the  wire  so  that  the  cur- 


Fio.  15. 

rent  flowrs  from  north  to  south.  Complete  the  circuit  and 
note  the  direction  of  the  swing  of  the  needle.  2.  Repeat 
with  the  wire  directly  under  the  needle.  3.  Repeat  1  with 
the  current  reversed,  that  is,  flowing  from  south  to  north 
over  the  needle.  4.  Repeat  2  with  the  current  flowing 
from  south  to  north.  5.  Place  the  compass  on  a  tumbler 


26  CURRENT  ELECTRICITY. 

or  block  of  wood  as  shown  in  Fig.  15.  Hold  the  wire 
vertically,  due  north  from  the  compass,  with  the  current 
flowing  down,  and  bring  it  slowly  up  to  the  north  pole. 
6.  Eepeat  5,  holding  the  wire  due  south  of  the  compass  and 
bring  it  up  to  the  south  pole.  7.  Invert  the  wire  so  that 
the  current  flows  up,  and  repeat  5.  8.  Repeat  6,  the 
current  flowing  up.  9.  Wind  the  wire  tightly  around  the 
compass  so  as  to  form  a  rectangle.  Hold  this  rectangle 
vertically  in  a  north  and  south  line  ;  place  the  compass  in 
the  centre  of  the  rectangle.  10.  Repeat  9  with  a  loop 
instead  of  a  rectangle.  11.  Observe  the  effect  of  using 
more  than  one  loop,  by  winding  the  wire  around  the  com- 
pass once,  then  5  or  6  times.  12.  Observe  the  effect  of  the 
size  of  the  loops.  Try  a  large  loop  and  a  small  one,  keep- 
ing the  compass  in  the  centre  of  each,  13.  Observe  the 
effect  of  the  distance  of  the  wire  from  the  needle. 

QUESTIONS. — 1.  Illustrate  each  case  by  means  of  a  dia- 
gram. 2.  What  conditions  affect  the  direction  of  the 
swing  of  the  needle  ?  3.  If  a  man  were  swimming  in  the 
current  so  that  it  enters  his  feet  and  leaves  his  head,  he 
always  facing  the  needle,  to  which  hand,  right  or  left, 
would  a  north-seeking  pole  be  urged  ?  *  A  south-seeking 
pole  ?  If  you  cannot  tell,  put  yourself  in  the  place  of  the 
imaginary  man  by  holding  the  wire  in  front  of  you,  or 
make  a  little  paper  man,  marking  the  right  and  left  hands, 
and,  holding  it  in  the  position  described,  move  it  around 
the  loop,  observing  towards  which  of  his  hands  the  north 
pole  of  the  needle  is  deflected.  In  marking  the  hands  of 
the  paper  man,  do  not  forget  that  if  he  faces  you  his 
hands  would  be  the  opposite  of  yours,  that  is,  his  left 
hand  would  be  opposite  your  right.  4.  What  conditions 
affect  the  amount  of  the  swing?  5.  Remembering  that 

*  Notice  that  we  are  dealing  here  wilh  poles,  not  with  entire 
magnets. 


ACTION  Off  CURRENTS  ON  MAGNETS.  27 

the  needle  always  tends  to  place  itself  in  the  line  of  mag- 
netic force,  from  a  study  of  the  diagrams  make  a  diagram 
of  the  field  of  force  around  a  wire  carrying  a  current. 

The  Galvanometer. — The  law  connecting  the  direction 
of  the  swing  of  the  needle  with  the  direction  of  the  cur- 
rent is  called  Ampere's  law.  Advantage  of  this  law  is 
taken  in  constructing  an  instrument  for  observing  the 
direction  and  strengths  of  electric  currents.  The  in- 
strument is  called  a  galvanometer,  and  consists  of  a 
magnetic  needle  placed  in  the  centre  of  a  coil  of  wire  and 
arranged  so  as  to  move  freely.  When  this  coil  is  placed  in 
a  north  and  south  line  and  a  current  is  passed  through  it, 
the  needle  is  deflected.  The  direction  of  the  deflection 
indicates  the  direction  of  the  current,  while  the  degree  of 
the  deflection  indicates  the  relative  strength  of  the  cur- 
rent. In  a  general  way,  the  stronger  the  current,  the 
greater  the  deflection. 

We  found  that  with  a  given  current  the  amount  of  deflec- 
tion could  be  changed  by  varying  the  number  of  turns  of 
wire.  In  most  galvanometers  this  is  done  by  changing 
the  connections.  With  a  very  heavy  current,  but  few 
turns  would  be  needed;  with  a  weak  current,  more  turns 
would  be  required  to  give  readable  changes  in  the  position 
of  the  needle  for  small  differences  in  current.  Of  course, 
in  comparing  various  currents,  the  same  number  of  turns 
must  be  used. 

Fig.  16  is  a  representation  of  a  galvanometer.  The  coil 
of  wire  Wis  wound  upon  -a  wooden  hoop,  H,  which  is  sup- 
ported in  an  upright  position  by  the  base-boards  E  and  D. 
This  coil  is  connected  with  the  three  binding-posts  B,  B', 
B".  Starting  from  B,  the  wire  passes  once  around  the 
hoop  and  is  led  out  to  B'.  It  then  is  wound  around  the 
hoop  nine  times  more,  so  that  if  B  and  B'  be  connected, 
the  current  passes  around  the  hoop  once  ;  if  B'  and  B" , 
the  current  passes  through  nine  turns;  while  if  B  and  B" 


28  CURRENT  ELECTRICITY. 

be  connected,  ten  turns  are  in  circuit.  A  compass  C 
placed  in  the  centre  of  the  hoop  furnishes  the  magnetic 
needle  whose  indications  are  observed,  the  scale  on  the 
compass  providing  a  means  or;  measuring  the  amount  of  the 


FIG.  16. 

swing.  A  galvanometer  is  represented  in  diagram  by  the 
small  figure  on  the  left.  This  sign  does  not  represent 
simply  this  form  of  galvanometer,  but  any  form. 

PRECAUTIONS. — 1.  The  compass  must  be  in  the  centre 
of  the  hoop.  2.  The  coil  must  be  in  a  north  and  south 
line.  3.  There  must  be  no  iron. or  magnets  near.  4.  All 
contacts  must  be  good.  5.  Before  reading  tap  the  hoop 
gently,  as  the  needle  may  stick.  6.  In  reading  hold  the 
eye  as  nearly  as  possible  vertically  over  the  needle.  7.  The 
end  of  the  needle  when  at  rest  should  be  directly  over  the 
zero  of  the  scale.  8.  When  using  the  galvanometer  con- 
nect it  for  ten  turns,  unless  the  instructions  state  other- 
wise. 


ELECTRICAL  RESISTANCE.  29 

To  READ  BY  "REVEBSAL." — As  getting  the  zero  of  the 
scale  just  under  the  end  of  the  needle  requires  quite  nice 
adjustment  and  takes  time,  it  is  better  to  read  the  instru- 
ment by  what  is  known  as  the  "reversal  method."  Adjust 
the  instrument,  having  the  coil  nearly  north  and  south  and 
the  zero  of  the  scale  within  five  degrees  or  so  of  the  posi- 
tion taken  by  the  end  of  the  needle  when  at  rest.  Close 
the  circuit,  read;  reverse,  and  read  again.*  The  average 
of  the  two  readings  will  be  the  true  deflection.  This 
method  saves  time  and  is  more  accurate.  It  should  be 
used  whenever  current  strengths  are  to  be  compared. 

EXERCISE  4. 

CONDITIONS  AFFECTING  ELECTRICAL  RESISTANCE. 

Preliminary. — When  a  circuit  is  so  arranged  that  the 
current  can  pass  entirely  through  it,  it  is  said  to  be 
"-closed,"  and  a  circuit  so  arranged  is  called  a  closed  cir- 
cuit. When  the  current  cannot  pass  at  any  point,  the  cir- 
cuit is  said  to  be  "open,"  or  "broken,"  and  such  a 
circuit  is  called  a  broken  or  open  circuit.  Connecting 
two  points  on  a  circuit  so  as  to  close  it  (e.g.  bringing 
the  ends  of  the  wires  together)  is  called  dosing  the 
circuit  or  making  the  circuit;  separating  two  parts  of 
a  closed  circuit,  so  as  to  open  it  (separating  the  ends  of 
the  wires,  lifting  one  plate  from  the  liquid,  etc.),  is 
called  breaking  the  circuit  or  breaking  contact.  Sep- 
arating two  parts  of  a  circuit  and  attaching  the  ends  to 
a  conductor  (as  a  wire  or  a  piece  of  apparatus),  so  as  to 
include  it  in  the  circuit,  is  called  introducing  that  bochj 
into  the  circuit. 

When  several  cells  are  arranged  so  as  to  give  a  current 

*  If  no  reverser  is  used,  this  may  be  done  by  changing  the  con- 
nections at  the  binding-posts. 


30  CURRENT  ELECTRICITY. 

they  are  called  a  galvanic  battery,  or  simply  a  battery. 
That  part  of  the  circuit  which  connects  the  plates  out- 
side of  the  vessel  is  called  the  external  circuit,  and  the 
part  inside  of  the  vessel  is  called  the  internal  circuit. 

We  have  already  observed  that  when  various  bodies 
were  inserted  in  the  external  circuit  of  the  same  cell,  and 
the  wires  were  laid  over  the  compass  at  the  same  dis- 
tance from  the  needle,  the  deflections  of  the  needle  were 
not  the  same.  We  have  also  learned  that  the  amount  of 
this  deflection  is,  under  similar  conditions,  taken  as  indi- 
cating the  strength  of  the  current.  We  naturally  infer  that 
all  bodies  do  not  possess  to  the  same  degree  the  property  of 
allowing  the  current  to  pass.  This  idea  is  expressed  by 
saying  that  the  relative  conductivity,  or,  more  commonly, 
the  resistance,  of  all  bodies  is  not  the  same.  A  body 
that  will  transmit  but  little  current  is  said  to  have  a  high 
resistance;  one  that  will  transmit  considerable  current  is 
said  to  have  a  low  resistance.*  Resistance,  then,  may  be 
taken  to  indicate  the  degree  to  which  a  body  possesses 
the  property  of  not  transmitting  the  current.  In  the  fol- 
lowing exercise  we  wish  to  find  out— 

1.  What  sort  of  bodies  have  high,  and  what  sort  low, 
resistance. 

2.  What  effect  length,  material,  and  cross-section  have  on 
the  resistance  of  bodies. 

EXPERIMENT    1. 

Apparatus.— For  Part  I :  Cell;  galvanometer  ;  connecting  wires  ; 
coil  of  copper  wire  ;  iron  nail ;  pieces  of  zinc  ;  carbon  ;  wood  ; 
glass  rod  ;  dilute  sulphuric  acid  and  water  ;  tumbler.  For  Part  II  : 
In  addition,  mercury  cups  ;  reverser  ;  wire  coils. 

OBJECT. — To  study  (1)  the  power  of  various  bodies  to 
transmit  the  current,  and  (2)  the  conditions  effecting  this 
power. 

*  Of  course,  under  the  same  conditions  regarding  cell,  distance 
of  wire  from  magnetic  needle,  etc, 


ELECTH1CAL  RESISTANCE.  31 

MANIPULATION'. — In  Fig.  17,  B  represents  a  cell  and  0  a 
galvanometer.  One  wire  from 
the  cell  connects   with   the 
binding-post  on  the  galvan- 
ometer.    A  wire  leads  from 


the  galvanometer  connected  FIG.  17. 

so  that  10  galvanometer-turns  are  in  circuit.  If,  now,  the 
ends  of  wires  xxf  are  pressed  on  any  substance,  the  circuit 
is  completed.  The  ends  of  the  wires  should  be  scraped 
bright  and  free  from  insulation,  and  all  contacts  made  per- 
fect. The  screws  in  the  binding-posts  should  press  firmly  on 
the  wires.  These  precautions  are  important.  Set  up  the  ap- 
paratus and  show  it  to  the  instructor  before  beginning  the 
experiment.  The  galvanometer  must  be  carefully  read 
according  to  the  instructions  already  given. 

Part  /. — Tabulate  the  results  of  inserting  the  following 
bodies, in  turn,  into  the  circuit:  iron,  copper,  zinc,  carbon, 
wood,  glass,  paper,  water,*  dilute  sulphuric  acid,  etc.,  re- 
cording results  as  follows: 

TABLE  I. 


Substance. 

Galvanometer  Reading. 

Part  II.— Introduce  the  mercury-cup,  M.  C.,  into  the 
circuit  by  attaching  the  ends  to  the  binding-posts,  one 
end  to  one  post,  as  in  Fig.  18.  To  introduce  coils  of  wire 
into  the  circuit,  dip  one  end  well  down  into  the  mercury  in. 
one  cup,  and  the  other  end  into  that  in  the  other  cup.  Lay 
the  card  on  which  the  coil  is  mounted  flat  on  the  table, 
and  bend  the  ends  of  the  wires  so  that  they  will  not  spring 
out  of  the  mercury  while  the  galvanometer  is  read.  When 

*  To  test  the  water,  place  the  naked  ends  of  the  wires  in  a  tumbler 
of  water.  Note  and  record  anything  going  on  in  the  tumbler,  as 
well  as  the  reading  of  the  galvanometer.  Then  add  to  the  water  10 
or  12  drops  of  sulphuric  acid,  and  repeat  your  observations. 


CURRENT  ELECTRICITY. 


two  single  ends,  a  a,  Fig.  19,  are  placed  in  the  cups, 
there  are  10  meters  of  wire  in  circuit.  When  one  single 
end,  a,  and  one  twisted  end,  b,  are  in  the  cups,  there  are 
5  meters  in  the  circuit.  The  coils  are  labelled,  and  cou- 


M.C. 

FIG.  18. 

sist  of,  1,  5  and  10  yards  No.  28  copper  wire  ;  2,  20  yards 
No.  28  copper  wire;  3,  5  yards  No.  24  (larger  cross-section) 
copper  wire ;  4,  5  yards  German-silver  wire,  No.  24  or  No. 
28,  as  labelled,  same  cross-section  as  one  of  the  coils  of 
copper  wire  of  5-meter  length.  Insert  in  turn  5,  10,  20 


FIG    19. 

yards  No.  28  copper  wire,  5  yards  No.  24  copper  wire, 
5  yards  German-silver  wire.     Record  results  in  : 

TABLE  II. 


Material. 

Length. 

Cross-section. 
(By  number.) 

Galv.  Read. 

ELECTRICAL  RESISTANCE.  33 

QUESTIONS. — Write  in  your  note-books  what  has  been 
learned  as  regards:  1.  The  equal  resistance  of  bodies. 
2.  The  sort  of  bodies  that  seem  to  have  the  highest  resistance, 
and  the  sort  that  seem  to  have  the  lowest.  3.  The  resist- 
ance of  water  and  the  effect  of  adding  acid.  4.  The  condi- 
tions affecting  the  resistance  of  a  body.  5.  The  reason  why 
the  wires  are  of  copper.  6.  The  reason  why  they  are  covered 
with  cotton,  etc.  t  7.  The  reason  why  the  covering  must  be 
removed  where  connections  are  made.  8.  Give  a  definition 
of  resistance.  9.  What  part  of  the  circuit  has  been  used 
in  this  experiment  ?  10.  Has  anything  been  observed  at 
the  ends  of  the  wires  on  making  and  breaking  circuit  ?  If 
so,  what?  11.  What  goes  on,  so  far  as  you  have  observed, 
when  the  current  is  passed  through  water  ?  Or  through 
water  and  acid  ?  12.  Arrange  the  names  of  all  the  bodies 
that  you  have  examined  in  a  list,  commencing  with  those 
of  the  highest  and  ending  with  those  of  the  lowest  resist- 
ance. Include  air  in  this  list. 

EXERCISE   5. 

ELECTRICAL  RESISTANCE. 

Preliminary. — If  we  wish  to  insert  more  than  one  con- 
ductor into  the  external  circuit,  connection  can  be  made  in 
two  ways;  either  end  to  end,  or  side  by  side,  as  in  Fig.  20. 


C7rsrr'~=~ *«*&*- 


FIG.  20. 


The  first  arrangement  is  called  connecting  in  series,  and 
the  second  connecting  in  parallel,  or  in  multiple  arc.     The 


34 


CURRENT  ELECTRICITY. 


question  is  naturally  suggested  whether,  with  the  same 
bodies,  it  makes  any  difference  to  the  total  resistance  of  the 
circuit  which  method  is  used.  Write  out  the  general 
method  *  of  an  experiment  to  answer  this  question,  outline 
a  special  method,  using  the  apparatus  of  the  preceding 
exercise,  and  give  the  reasons  for  the  use  of  each  part  of 
the  apparatus.  Prepare  a  diagram  showing  the  relation  of 
the  parts,  connections,  etc. 


EXPERIMENT  1. 

Apparatus.—  The  same  as  in  Ex.  4  (reverser)  shown  in  Fig.  21,  the 
mercury -cups  being  used  to  insert  the  various  conductors  in  the  cir- 
cuit. 


M.C. 
FIG.  21. 


*  The  general  method  is  a  brief  statement  of  the  bodies  experi- 
mented upon  and  of  the  conditions  under  which  they  must  be  placed 
in  order  to  fulfil  the  object  of  the  experiment.  As  different  forms 
of  the  bodies  may  be  used,  and  as  the  required  conditions  may  be 
brought  about  by  various  means,  the  special  method  is  a  statement 
of  just  what  forms  of  the  bodies  are  used  and  just  how  these  forms 
are  placed  under  the  conditions  required  by  the  experiment.  The 
general  method  might  be  taken  as  the  plan  and  the  special  method 
as  the  particular  way  in  which  the  plan  is  carried  out. 


ELECTRICAL  RESISTANCE. 


35 


OBJECT. — To  see  if  the  manner  in  which  conductors  are 
placed  in  the  external  circuit  affects  the  resistance  of  the 
circuit. 

MANIPULATION. — Part  I.  Place  in  the  circuit  20  meters 
No.  28  copper  wire.  Observe  the  deflection.  Remove  one 
end,  attach  to  it,  by  twisting,  one  end  of  the  10-meter  coil 
of  No.  28  copper  wire,  and  place  the  free  end  of  the  IO- 
meter coil  in  the  mercury-cup.  There  are  now  in  all  30 
meters  No.  28  wire  in  the  circuit.  Observe  the  deflection. 
Add  to  the  other  two  coils  the  coil  of  No.  24  copper  wire. 
Insert  also  the  coil  of  German-silver  wire.  Record  results 
as  follows: 

TABLE  I. 


No.  of  Trial. 

Lengths  and  Substances  Used. 

Galvanometer  Reading. 

Right. 

Left. 

Average 

Part  II.  Place  the  coil  of  German-silver  wire  in  the 
circuit  and  read  the  galvanometer.  Without  removing 
the  first  coil,  also  put  in  the  circuit  the  20  meters  of 
copper  wire.  The  current  can  now  pass  through  both 
coils  at  the  same  time.  Read  the  galvanometer.  Also 
place  in  the  circuit  5  meters  No.  24  copper  wire,  in  addition 
to  the  others.  Record  the  results  as  above.  Great  care 
must  be  used  in  securing  the  contacts  in  the  mercury- 
cups,  and  all  precautions  should  be  taken  to  get  as  accu- 
rate galvanometer-readings  as  possible. 

QUESTIONS. — 1.  What  effect  is  produced  on  the  resist- 
ance of  the  external  circuit  by  introducing  conductors  (a) 
in  parallel  ?  (b)  In  series  ?  2.  Explain  this  result  from 
the  knowledge  obtained  in  the  preceding  exercise.  3.  Can 
the  external  circuit  be  composed  of  more  than  one  sort  of 
material  ? 


36 


CURRENT  ELECTRICITY. 


EXERCISE  6. 

METHODS  OF  CONNECTING  GALVANIC  CELLS. 

Preliminary. — When  more  than  one  cell  is  to  be  used, 
there  are  two  ways  of  connecting  them  ;  as  in  Fig.  22,  where 

the  positive  plate  of 
one  is  connected  with 
the  negative  plate  of 
the  next;  or,  as  in  Fig. 
23,  where  all  the  posi- 
tives are  connected  by 
one  wire  and  all  the 
negatives  by  the  other. 
The  former  method 
is  called  connecting  in 
series;  the  latter,  con- 
necting in  parallel,  or 
multiple.  Now,  the 
external  resistance 
may  be  either  com- 
paratively high  or  low. 
For  instance,  the  con- 
ductor may  be  a  short, 
thick  piece  of  copper 
wire,  or  a  considerable  length  of  fine  German-silver  wire. 
Hence  it  is  a  matter  of  some  consequence  to  know  which 
method  of  connection  gives  the  most  current,  (a)  when  the 
external  resistance  is  high,  and  (b)  when  it  is  low. 

EXPERIMENT  I. 

Apparatus. — Two  cells;  galvanometer;  reverser;  mercury-cups; 
short  piece  of  thick  copper  wire;  connecting  wires  (connecter,  if 
available);  wire-coil  for  high  resistance. 

OBJECT. — To  determine  which  method  of  connecting  cells 
gives  the  most  current,  (a)  when  the  external  resistance  is 
high,  and  (b)  when  it  is  low. 


METHODS  OF  CONNECTING  GALVANIC  CELLS.     37 


MANIPULATION. — Insert  a  galvanometer  (one  turn)  and 
mercury-cups  into  the  circuit  of  a  single  cell,  as  in  Fig.  24. 
Connect  the  two  mercury-cups  with  a  short  piece  of  copper 
wire  and  read  the  galvanometer.  Disconnect  the  wire 
leading  from  the  cell  to  the  binding-post  of  the  mercury- 
cup  (marked  a  in  Fig.  24),  and  by  means  of  the  connecter, 


or  by  twisting  the  ends  of  the  wires  together,  connect  it  with 
the  wire  leading  from  the  opposite  element  of  the  second 
cell.  Attach  the  other  wire  of  the  second  cell  to  the  empty 
binding-post  of  the  mercury-cup.  There  are  now  two  cells 
in  circuit,  the  carbon  of  one  connected  with  the  zinc  of  the 
other— that  is,  the  cells  are  in  "series,"  as  in  Fig.  25. 
Connect  the  mercury-cups  with  the  short  piece  of  wire  and 
read  the  galvanometer.  The  resistance  of  the  external  cir- 
cuit is  that  of  the  connecting  wires,  the  galvanometer  con- 
nection, the  mercury  in  the  mercury-cup,  and  the  short 
piece  of  wire  connecting  them;  and  as  these  are  all  good 
conductors,  large  and  short,  the  total  resistance  of  the  ex- 
ternal circuit  is  very  small. 

Take   out   the  short   piece   of   copper   wire  connecting 
the  mercury-cups,  and  put  in   its  place  a  coil  of  Ger- 


38 


CURRENT  ELECTRICITY. 


man-silver  wire  or  20  meters  of  No.  28  copper  wire. 
This  makes  the  resistance  of  the  external  circuit  quite 
high.  Change  the  galvanometer  connections  so  as  to  have 
ten  turns,  and  read  the  instrument.  Leaving  the  coil  of 


FIG.  25. 

wire  in  the  circuit,  disconnect  cell  No.  2  (B,)  and  con- 
nect cell  No.  1  (B2)  alone  with  the  mercury-cups.  Read 
the  galvanometer. 

Connect  the  carbon  plates  of  both  cells  with  a  wire  lead- 
ing to  the  galvanometer,  as  in  Fig.  26.  In  the  same  way 
connect  both  zinc  plates  with  the  same  binding-post  on  the 


G.S.  Wire 


FIG.  26. 

mercury-cup.  The  two  cells  are  now  connected  in  "paral- 
lel." Read  the  galvanometer.  Replace  the  coil  of  wire  in 
the  mercury-cup  by  the  short  copper  wire.  Connect  the 
galvanometer  for  one  turn  and  read  it.  Arrange  results  as 
follows : 


METHODS  OF  CONNECTING  GALVANIC  CELLS.     39 

TABLE. 


No.  of  Cells. 

How  Connected. 

External  Resist. 

Galv-read. 

1 

High 

R. 

L. 

Av. 

2 

Series 

44 

2 

Parallel 

« 

1 

Low 

2 

Series 

« 

2 

Parallel 

<« 

The  cases  in  the  table  are  not  arranged  as  they  are  tried 
in  the  experiment.  The  table  arrangement,  however,  makes 
it  much  easier  to  compare  results.  The  table,  made  out 
in  this  way,  should  be  placed  in  the  note-book,  and  as 
the  different  cases  are  tried  the  galvanometer  readings 
obtained  can  be  placed  where  they  belong  in  the  last  col- 
umn. From  the  study  of  the  table,  which  arrangement  of 
cells  seems  to  give  the  most  current  when  the  external  re- 
sistance is  high  and  which  when  the  external  resistance  is 
low  ? 

Unit  of  Resistance. — If  resistances  are  to  be  compared 
accurately,  a  standard  of  resistance  is  needed.  As  we 
have  found  that  resistance  depends  on  length,  cross-section, 
and  material,  we  can  get  a  standard  of  resistance  by  taking 
a  specified  length  of  a  specified  body  of  a  specified  cross-sec- 
tion. When  the  body  used  is  mercury,  cooled  to  the  freez- 
ing-point of  water,  the  length  about  1  meter,  and  the 
cross-section  1  sq.  millimeter,  the  resistance  is  said  to  be 
1  ohm.  Any  body  having  a  resistance  equal  to  that  of  the 
standard  mercury  column  is  said  to  have  a  resistance  of  1 
ohm. 

Resistance-box.  —  The  instrument  commonly  used  in 
measuring  resistance  is  called  a  resistance-box  or  rheostat. 
It  is  an  arrangement  by  which  different  coils  of  wire  of 
known  resistance  may  be  placed  in  the  circuit.  A  com- 
mon form,  together  with  a  sign  for  a  diagram,  is  shown 


40 


CURRENT  ELECTRICITY. 


in  Fig.  27.  It  consists  of  a  wooden  box  provided  with 
three  switches.  A  number  of  metallic  heads  are  placed  in 
semicircles  about  the  pivots  of  the  switches.  Each  head 
is  furnished  with  a  number  which  indicates  the  resistance 


FIG.  27. 

in  the  circuit  when  the  end  of  the  switch  rests  on  that 
head.  One  switch  (the  one  at  the  right  in  Fig.  27)  places 
from  0  to  1  ohm  in  the  circuit,  the  second  from  1  to  10 
ohms,  and  the  third  from  10  to  100  ohms.  By  using  all 
three  switches,  any  resistance  from  0  to  111  ohms  may 
be  placed  in  the  circuit,  The  sum  of  the  readings  of  the 
three  switches  is  taken  as  the  measure  of  the  resistance  ; 
for  example,  in  the  figure  the  box  reads  55.9  ohms.  The 
box  has  two  binding-posts  for  making  connections. 


EXERCISE  7. 

RELATIVE  RESISTANCE. 


Preliminary. — In  the  following  experiment  we  wish  to 
find  the  lengths  of  iron  and  copper  wire  equivalent  in  re- 
sistance to  1  centimeter  of  German-silver  wire.  We  must 
place  a  known  length  of  German-silver  wire  in  the  cjr- 


RELATIVE  RESISTANCE. 


41 


cuit,  observe  the  deflection  of  the  galvanometer,  and  then 
find  the  lengths  of  the  wires  of  other  materials  required 
to  produce  the  same  deflection  of  the  galvanometer.  We 
will  use  the  apparatus  indicated  in  Fig.  28. 

The  board  A  carries  two  uprights,  BB,  which  support  a 
meter-stick,  M.  Stretched  between  these  upright,  is  a  piece 
of  uncovered  German-silver  wire,  on  which  slides  a  hook 
made  of  the  end  of  one  connecting-wire.  Above  the  Ger- 
man-silver wire  the  iron  and  copper  wires  are  stretched 
between  the  uprights,  passing  back  and  forth  several  times. 
A  binding-post,  a,  is  connected  with  one  end  of  all  three 


FIG.  28. 


sets  of  wires.  When  the  circuit  is  completed  from  the 
binding-post  a,  through  the  wire  and  the  hook  that  slides 
on  it,  the  length  of  wire  in  the  circuit  will  be  determined 
by  the  length  of  wire  between  a  and  the  hook,  as  read  on 
the  meter-stick,  and  can  be  varied  by  sliding  the  hook  along 
the  wire,  so  varying  the  resistance.  (Experiment  4,  Part 
II.)  More  than  one  meter  of  the  wire  may  be  placed  in 
circuit  by  attaching  the  hook  to  the  wire  running  back  to 
the  right-hand  upright.  The  total  length  of  wire  in  the 
circuit  in  each  case  will  be  the  whole  length  which  the 
current  passes  through  in  going  from  the  binding-post  to 
the  hook, 


CURRENT  ELECTRICITY. 


EXPERIMENT. 

Apparatus.— Cell;  rack  with  wires  (Fig.  28);  reverser;  galvanome- 
ter ;  connecting-wires.* 

OBJECT. — To  find  what  length  of  iron  and  copper  wires 
give  a  resistance  equivalent  to  that  of  one  centimeter  of 
German-silver  wire. 

MANIPULATION. — Having  set  up  the  cell  and  connected 
the  galvanometer  for  ten  turns,  introduce  the  German- 
silver  wire  into  the  circuit,  by  attaching  one  connecting 
wire  to  the  binding-post  a  and  connecting  the  wire  leading 
from  the  hook  with  the  other  element  of  the  cell.  The 
distance  from  the  hook  to  the  binding  post,  as  read  on  the 
meter-stick,  gives  the  length  of  German-silver  wire  in  the 
circuit.  Observe  the  galvanometer-reading  with  50  cm.  of 
wire  in  the  circuit,  then  remove  the  hook  from  the  German- 
silver  wire,  place  it  on  the  iron  wire,  and  find  by  trial  the 
position  which  gives  the  same  galvanometer-reading.  Re- 
peat the  operation  with  the  copper  wire,  recording  the  total 
lengths  in  circuit  in  each  case.  Now,  starting  with  40  cm. 
of  German-silver  wire,  again  find  corresponding  lengths 
of  iron  and  copper  wire.  Try  some  other  lengths  if  time 
allows.  Tabulate  results  as  follows : 


G.S.  wire. 

Galv.-read. 

Iron  wire. 

Copper  wire. 

Iron  wire 
equal  to 
1  cm.  G.-S. 

Copper  wire 
equal  to 
1  cm.  G.-S. 

R. 

L. 

Av. 

EXERCISE  8,  A. 

MEASUREMENT  OF  RESISTANCE. 

Preliminary. — The  purpose  of  the  following  exercise  is 
to  determine  the  resistance  of  a  body  by  what  is  called  the 
"  method  of  substitution."  This  method  is  based  upon 

*  Que  witU  book,  or  a.u  "English"  binding  post, 


MEASUREMENT  OF  HR8I8TAN08,  4B 

the  fact  that  bodies  of  equal  resistance  introduced  into  the 
same  circuit  will  transmit  the  same  amount  of  current. 
We  find  the  resistance  in  ohms  of  a  body  which  will 
transmit  the  same  amount  of  current  transmitted  by  a 
body  of  unknown  resistance.*  The  apparatus  used  is  as 
shown  in  Fig.  29.  A  galvanometer,  G,  a  resistance-box,. 72, 
and  mercury-cups,  mm,  are  connected  in  the  circuits  of  a 


FIG.  29. 

cell,  B.  The  mercury-cups  afford  a  means  of  easily  insert- 
ing a  body  into  the  circuit.  On  replacing  the  body  by  a 
piece  of  thick  copper  wire  the  resistance  of  the  mercury 
cups  is  practically  reduced  to  0,  which  is  equivalent  to 
taking  them  out  of  the  circuit.  By  setting  the  switches 
of  the  resistance-box  at  0,  that  also  is  practically  taken  out 
of  the  circuit,  so  that  it  is  not  necessary  to  disconnect  it 
when  the  current  is  passed  through  the  body. 

EXPERIMENT. 

Apparatus.— Cell;  resistance-box;  galvanometer;  connecting- wire; 
conductor  whose  resistances  are  to  be  measured;  mercury-cups; 
reverser. 

OBJECT. — To  determine  the  resistance  of  a  body  in  ohms 
by  the  method  of  substitution. 


*  Let  the  pupil  prepare  a  statement  of  the  conditions  necessary  for 
carrying  out  such  an  experiment. 


44 


CURRENT  ELECTRICITY. 


MANIPULATION. — Having  all  three  switches  of  the  re- 
sistance-box on  the  zero-point  (that  is,  having  no  resist- 
ance in  the  box),  connect  the  mercury-cups  by  each,  in  turn, 
of  the  coils  of  wire  whose  resistance  is  required,  and  read 
the  galvanometer.*  Replace  the  coil  by  the  short  piece  of 
copper  wire  (so  that  the  mercury-cups  offer  practically  no 
resistance),  bring  your  eye  directly  over  the  galvanometer- 
needle,  and,  without  looking  at  the  box,  turn  the  10-ohm 
switch  until  the  galvanometer  reads  as  close  to  the  former 
reading  as  you  can  get,  that  is,  until  the  addition  of  an- 
other 10  ohms  makes  it  too  low.  Adjust  now  the  ohm 
switch  in  the  same  manner,  and  lastly  the  0. 10-ohm  switch. 
The  adjustment  of  the  switches  should  be  done  with  the 
right  hand,  the  eye  being  kept  constantly  on  the  needle. 
Read  the  resistance  in  the  box.  This  is  equal  to  the  re- 
quired resistance  of  the  coil  of  wire.  Repeat  with  the 
same  coil,  being  careful  not  to  look  at  the  box  so  that  your 
second  trial  may  not  be  biased  by  the  results  of  the  first. 
Determine  in  this  way  the  resistance  of  several  coils  of 
wire.  Record  as  follows : 


Length. 

Material. 

Galv.  -reading. 

Resistance. 

No.  of  Wire. 

R. 

L. 

Av. 

*  As  all  that  is  needed  is  to  get  the  same  galvanometer-reading,  it 
is  not  necessary  to  reverse  the  galvanometer.  In  this  case,  however, 
all  deflections  must  be  on  the  same  side.  The  first  and  second  read- 
ings should  be  taken  in  as  rapid  succession  as  possible,  in  order  to 
decrease  the  effect  of  any  possible  change  in  the  current. 


MEASUREMENT  Off  RESISTANCE.  45 

EXERCISE  8,  B. 

MEASUREMENT  OF  RESISTANCE. 

Preliminary. — When,  in  such  an  apparatus  as  Fig.  30  rep- 
resents, the  current  of  the  battery  B  comes  to  the  point  a, 
it  divides,  part  going  down  the  side  abd  and  part  down  the 
side  acd.  If  the  resistances  of  the  two  sides  are  alike,  the 
same  amount  of  current  will  flow  through  each ;  but  if  they 
are  not  alike,  more  current  will  follow  the  side  having  the 
less  resistance.  If  we  attach  wires  at  the  points  b  and  c 
and  connect  them  with  the  galvanometer,  so  long  as  the 
same  amount  of  current  passes  on  each  side  the  galvanome- 
ter will  not  be  affected ;  but  if  the  resistance  of  one  side 


FIG.  30. 

be  made  greater  than  that  of  the  other,  then  the  current 
will  flow  through  the  galvanometer  from  the  side  carrying 
the  greater  current.  Suppose  we  insert  in  cd  a  resistance- 
box,  and  in  bd  the  body  whose  resistance  we  wish  to  meas- 
ure, x.  If  the  resistance-box  is  at  0,  the  resistance  of  x 
will  hold  back  the  current  in  bd,  and  a  portion  of  it  will 
flow  from  b  to  c  through  the  galvanometer,  which  will  be 
deflected.  Suppose  now  we  increase  the  resistance  in  the 
box  until  the  galvanometer  reads  0,  then  we  know  that  the 
resistance  of  acd  equals  the  resistance  of  abd  (since  the 
wires  of  which  the  instrument  are  constructed  have  practi- 


46 


CURRENT  ELECTRICITY. 


cally  no  resistance),  and  that  the  required  resistance  of  x 
equals  the  known  resistance  in  the  box. 

Wheatstone's  Bridge. — On  a  board  is  placed  a  square  of 
wire,  abed,  Fig.  31,  with  a  binding-post  at  each  corner. 


The  sides  Id  and  dc  are  cut,  and  two  binding-posts  inserted 
in  each.  From  the  binding-posts  b  and  c  wires  (dotted 
lines)  are  led  to  the  galvanometer  6r,  and  the  battery-wires 
are  attached  to  the  binding-posts  a  and  d.  In  the  battery- 


I 


I 


FIG.  3-2. 


circuit  is  placed  a  key,  K,  which  closes  the  circuit  when 
depressed.  A  similar  key,  K' ,  is  placed  in  the  galvanom- 
eter-circuit. The  substance  to  be  tested,  x9  is  attached 


MEASUREMENT  OF  &ESISTANCE.  47 

to  the  binding-posts  gh,  and  the  resistance-box,  R,  is  con- 
nected at  ef.  Fig.  32  is  a  picture  of  the  same  apparatus 
when  ready  for  use. 

EXPERIMENT. 

Apparatus.— Wheatstone's  Bridge;  cell;  galvanometer;  two  con- 
tact-keys; resistance-box;  bodies  whose  resistances  are  to  be  meas- 
ured; bar-magnet;  connecting-wires. 

OBJECT. — To  determine  the  resistance  of  a  body  by  the 
use  of  Wheatstone's  Bridge. 

MANIPULATION*. — Connect  the  binding-posts  gli,  Fig.  31, 
by  the  substance  whose  resistance  is  required.  Close  the 
battery-circuit.  Then  close  the  galvanometer-circuit  for 
an  instant  only,  and  observe  the  direction  of  the  "  throw" 
of  the  galvanometer-needle.  Add  resistances,  observing 
the  throw  of  the  galvanometer-needle  after  each  addition, 
until  it  begins  to  move  the  other  way.  Then  work  down 
with  the  resistance-box  until,  on  closing  both  circuits,  no 
tremble  of  the  needle  is  observed.  The  resistance  in  the 
box  is  then  equal  to  the  unknown  resistance. 

PRECAUTIONS. — 1.  Avoid  throwing  the  galvanometer- 
needle  violently.  This  may  be  avoided  by  closing  the  gal- 
vanometer-circuit only  for  an  instant  until  there  are  such 
resistances  in  the  box  that  the  galvanometer-needle  scarcely 
moves.  A  longer  contact  is  then  safe.  2.  Always  close 
the  battery-circuit  before  closing  the  galvanometer-circuit. 
3.  Be  sure  that  all  contacts  are  good. 

During  the  first  part  of  the  experiment  the  motion  of 
the  needle  may  be  very  much  deadened  by  placing  a  bar- 
magnet  due  north  of  the  needle,  in  a  north  and  south  line, 
with  its  south  pole  near  the  north  pole  of  the  needle. 
During  the  latter  part  of  the  experiment  the  magnet  may 
be  removed.  The  presence  of  the  magnet  also  tends  to 
prevent  the  needle  from  oscillating,  and  saves  time  lost  in 
waiting  for  the  needle  to  come  to  rest  after  each  trial. 


48  CURRENT  ELECTRICITY. 

EXERCISE  9. 

ELECTRO-MOTIVE  FORCE. 

Preliminary. — We  have  observed  that  bodies  differ  from 
one  another  in  resistance  to  an  electric  current,  and  have 
also  noted  the  conditions  upon  which  this  resistance  de- 
pends. Suppose,  now,  we  place  the  same  body  in  various 
circuits,  will  it  always  transmit  the  same  amount  of  cur- 
rent ?  That  is,  have  all  currents  the  same  power  of  over- 
coming a  given  resistance?  Let  us  see  if  the  conditions 
under  which  the  current  is  generated  make  any  difference. 
For  this  purpose  try  plates  of  various  materials  in  the  cell, 
being  careful  that  they  are  the  same  size  and  distance 
apart,  and  that  the  external  circuit  is  the  same.  With  a 
galvanometer  connected,  we  can  see  if  the  currents  gener- 
ated all  have  the  same  power  of  overcoming  resistance. 

EXPERIMENT. 

Apparatus. — Tumbler-cell;    plates  of   iron,    lead,    copper,  with 
leadiug-wires;  galvanometer;  reverser. 

OBJECT. — (1)  To  see  if  all  currents  have  the  same  power 
of  overcoming  resistance.  (2)  To  study  the  conditions  af- 
fecting this  power. 

MANIPULATION. — Lay  one  of  the  plates  on  the  table,  put 
on  it  two  little  pieces  of  wood,  lay  the  other  plate  on  them, 
slip  a  rubber  band  around  the  whole,  and  place  in  the 
liquid  in  the  tumbler.  Connect  the  galvanometer,  ad- 
justed for  ten  turns,  close  the  circuit,  and  resul  the  galva- 
nometer. If  a  reverser  is  available,  use  it;  if  not,  reverse 
by  changing  connections.  Try  the  cases  given  in  the  fol- 
lowing table,  and  any  others  that  you  can. 

The  plates  in  each  case  being  the  same  size  and  distance 
apart,  and  the  external  circuit  the  same,  the  resistance  is 
practically  alike  in  each  trinl.  From  the  study  of  the  re- 


FORCE. 


49 


Positive  Plate. 

Negative  Plate. 

Galv.-reading. 

R. 

L. 

Av. 

Copper 

Carbon 

Carbon 

Zinc 

«« 

Iron 

Iron 

Lead 

Carbon 

M 

Lead 

Zinc 

Carbon 

Carbon 

Zinc 

Zinc 

Copper 

.< 

•« 

Iron 

« 

Lead 

« 

Copper 

suits  obtained,  what  do  you  infer  regarding  (1)  the  power 
of  different  currents  to  overcome  resistance,  and  (2)  the 
conditions  affecting  this  power? 

QUESTIONS. — Why  are  zinc  and  carbon  usually  used 
in  galvanic  cells  ?  Would  zinc  and  copper  do  as  well  ? 
Why  not  use  iron  ?  What  conditions  seem  to  affect  the 
results  observed? 

Supplementary.— The  power  possessed  by  a  current  of 
overcoming,  or  the  power  that  pushes  the  current  through 
the  resistance,  is  said  to  be  due  to  the  Electro-motive  Force 
(often  written,  for  brevity,  E.  M.  F.).  The  higher  the 
E.  M.  F.,  the  more  current  will  pass  through  a  given  re- 
sistance, and  the  lower  the  E.  M.  F.,  the  less  current  will 
pass  through  the  same  resistance.  In  a  general  way,  the 
idea  of  electro-motive  force  corresponds  to  the  "head"  of 
water  in  a  pipe;  that  is,  to  the  pressure  which  pushes  the 
water  through  the  pipe.  The  higher  the  pressure,  the 
more  water  will  pass  through  the  pipe;  and  the  lower  the 
pressure,  the  less  will  pass  through  the  same  pipe. 

In  the  measurement  of  E.  M.  F.,  the  standard  is  very 
nearly  that  given  by  a  gravity-cell  (zinc  and  copper  in 
solutions  of  blue  and  white  vitriol).  The  amount  of  cur« 


60  CVRRBNT  ELECTRICITY. 

rent  generated  by  the  cell  under  test  that  will  pass  through 
a  resistance  is  measured  and  compared  with  the  amount 
that  passes  when  a  standard  cell  is  used. 

QUESTIONS. — 1.  Which  gives  the  greater  E.  M.  F.,  car- 
bon and  zinc,  or  iron  and  zinc  ?  2.  What  E.  M.  E.  is  pro- 
duced by  two  like  plates  ?  3.  What  seems  to  determine 
the  E.  M.  F.  in  a  galvanic  cell  ? 

EXERCISE  10. 

ELECTRO-MAGNETISM. 

EXPERIMENT    1. 

Apparatus. — Carriage-bolt ;  100  cm.  No.  18  wire  ;  cell ;  compass  ; 
iron-filings  ;  paper  and  pencil ;  current;  some  means  of  varying 
resistance  of  the  circuit  and  of  reversing  the  current. 

OBJECT. — To  study  the  magnetic  effects  of  an  electric 
current  and  the  conditions  affecting  the  strength  of  an 
electro-magnet-. 

MANIPULATION. — Part  L  Hold  the  carriage-bolt  in 
front  of  you  with  the  nut  away  from  you  and  wind  around 
it  15  or  20  turns  of  insulated  wire  from  left  to  right  (if  a 
watch  were  facing  you,  the  turns  would  be  with  the  direc- 
tion of  the  motion  of  the  hands).  Arrange  as  in  Fig.  33. 


FIG.  33. 

Complete  the  circuit.  Note  what  happens.  Test  the 
other  end  at  the  compass.  Move  the  compass  along  from 
one  end  of  the  bolt  to  the  other.  Note  what  happens  to  a 
piece  of  soft  iron  when  a  wire  carrying  a  current  is  coiled 
around  it. 

Part  1L     Repeat  Part  I  with  the  current  reversed. 


ELECTRO- MA  GNETISM.  51 

Part  IH.  Rewind  the  wire  in  the  opposite  direction, 
repeat  Part  I,  and  observe  the  result. 

Part  IV.     Reverse  the  current,  and  again  repeat. 

QUESTIONS. — 1.  What  is  the  effect  of  reversing  the  cur- 
rent ?  2.  What  effect  has  the  direction  of  the  current  ? 
3.  What  happens  when  the  circuit  is  broken?  Does  the 
effect  produced  by  the  direction  of  the  current  entirely 
disappear  when  the  circuit  is  broken  ? 

EXPERIMENT    2. 

OBJECT. — To  see  if  an  electro- magnet*  resembles  an 
ordinary  magnet. 

MANIPULATION. — Bring  the  electro-magnet  up  to  some 
iron-filings,  and  see  if  it  attracts  them. 

EXPERIMENT    3. 

OBJECT. — To  investigate  the  conditions  affecting  the 
power  of  an  electro-magnet. 

MANIPULATION. — Lay  a  sheet  of  paper  on  the  table, 
place  the  electro-magnet  on  it,  and  draw  a  pencil-line 
around  the  magnet  so  as  to  mark  its  position  on  the 
paper,  f  Place  the  compass  about  east  of  one  pole  of  the 
electro-magnet,  and  at  such  a  distance  that  when  the  cur- 
rent is  turned  on  the  magnet  pulls  the  compass-needle 
around  15  or  20  degrees.  Mark  this  position  also. 
Change  the  current  by  varying  the  resistance  in  the 
circuit.  Has  the  strength  of  the  current  any  effect  on  the 
strength  of  the  magnet?  Put  as  many  more  turns  on  the 
magnet  as  yon  have  already.  Observe  the  results.];  What 
effect  has  the  number  of  turns  ?  Give  diagrams. 

*  A  piece  of  iron  magnetized  as  in  Exp.  1,  by  au  electric  current, 
is  called  an  electro-magnet. 

f  This  precaution  is  taken  in  order  that  the  distance  from  the 
magnet  to  the  compass  may  be  kept  the  same  Of  course,  for  each 
test,  both  magnet,  and  compass  must  be  on  the  marks. 

|  In  comparing  the  effects  of  different  numbers  of  turns,  the  same 
current  should  be  used. 


CURRENT  ELECTRICITY. 


QUESTIONS. — 1.  What  must  be  done  in  order  to  obtain 
an  electro-magnet  ?  2.  What  determines  the  nature  of 
the  poles  ?  3.  What  determines  the  strength  of  the  mag- 
net? 

EXERCISE   11. 

INDUCED     CURRENTS. 

Preliminary. — Arrange    the    apparatus  as  in   Fig.   34, 

•f  - 


FIG.  34. 

where  the  electro-magnet,  A,  is  placed  in  the  circuit,  into 
which  is  also  introduced  the  reverser,  It.  The  ends  of  the 
coil  of  a  second  electro-magnet,  B,  are  connected  by 
flexible  wires  with  the  sensitive  galvanometer,  G. 

When  the  current  passes  around  A  it  becomes  a  magnet} 
and,  if  B  is  placed  upon  it,  B  becomes  an  induced  mag- 
net. Hence  when  the  current  is  sent  into  A  the  result  is 
equivalent  to  thrusting  a  magnet  suddenly  into  the  coil  7>, 
whose  ends  are  connected  with  the  galvanometer.  By 
means  of  the  reverser,  the  poles  of  A  may  be  suddenly 
changed,  and  the  same  effect  produced  as  if  the  magnet 
in  B  were  suddenly  withdrawn,  turned  end  for  end,  and 
replaced  in  the  coil.  Slowly  separate  A  and  B  and  the 
effect  is  equivalent  to  slowly  withdrawing  the  magnet  from 
the  coil  B.  Bring  them  slowly  together,  and  the  opposite 
effect  is  produced, 


INDUCED   CURRENTS.  .     53 

EXPERIMENT   1. 

Apparatus.— Two  electro-magnets;  a  strong  current;  connecting- 
wires;  galvanometer;  reverser;  means  of  making  and  breaking  the 
circuit,  and,  if  possible,  some  means  of  varying  current  strength; 
clamp  to  suspend  one  coil. 

OBJECT. — To  observe  the  results  of  suddenly  thrusting  a 
magnet  into  a  coil  of  wire. 

MANIPULATION.— Place  B  upon  A.  When  the  galva- 
nometer-needle is  at  rest,  suddenly  close  the  circuit  of  A 
(that  is,  suddenly  introduce  a  magnet  into  B).  Observe 
and  record  carefully  the  behavior  of  the  needle. 

EXPERIMENT    2. 

OBJECT. — To  observe  the  effect  of  withdrawing  the  mag- 
net from  the  coil. 

MANIPULATION. — While  the  current  is  passing  through 
A  and  the  galvanometer-needle  is  at  rest,  break  the  circuit 
of  A.  Observe  and  record  as  above, 

EXPERIMENT    3. 

OBJECT. — To  investigate  the  effect  of  the  nature  of  the 
pole  used. 

MANIPULATION. — Change  the  reverser  and  turn  on  the 
current  in  A.  The  poles  of  A,  and  hence  those  of  the 
induced  magnet  in  B,  will  be  reversed.  Observe  results. 

EXPERIMENT    4. 

OBJECT. — To  observe  the  effect  of  moving  a  coil  of  wire 
with  an  iron  core  in  the  field  of  a  magnet. 

MANIPULATION. — Remove  the  coil  B  from  A.  Close 
the  circuit  of  A,  and  then  move  B  up  to  and  away  from  A, 
in  various  directions  and  with  various  speeds.  Observe 
the  galvanometer  indications  carefully  in  each  case,  with  a 
view  to  stating  the  conditions  affecting  the  amount  of  cur- 
rent, its  direction,  etc.  If  practicable,  change  the  strength 
of  the  current  through  A  to  see  if  the  strength  of  the 


54:  CURRENT  ELECTRICITY. 

magnetic  field  makes  any  difference.     Tabulate  results  as 
follows : 


How  B  was  moved. 


Direction  of 
Galvanometer-reading:. 


Amount  of  Galv.- 
reading. 


In  the  first  column  insert  the  words  "towards  A"  "away 
from  A"  "in  a  horizontal  circle  above  A"  as  the  case 
may  be.  In  the  second  column  insert  the  words  "right" 
or  "left/'  as  the  case  may  be.  In  the  third  column,  the 
words  "  more,"  "  less,"  etc. 

QUESTIONS. — 1.  Is  it  possible  to  obtain  electricity  by  the 
use  of  magnets  ?  2.  What  conditions  have  you  found  to 
be  necessary  ?  3.  What  conditions  have  you  observed  to 
affect  the  amount  of  the  current,*  and  its  direction? 
4.  Would  it  be  possible  to  construct  a  machine  on  this 
principle  which  could  be  used  to  produce  a  current  of 
electricity?  5.  What  would  be  the  essential  parts  of  such 
a  machine? 

A  mechanical  contrivance  for  fulfilling  these  conditions, 
and  thus  generating  electricity  from  motion,  is  called  a 
Dynamo-electric  Machine,  or  simply  a  Dynamo. 

EXPERIMENT    5. 

OBJECT. — To  see  if,  reversing  the  last  process,  motion 
can  be  obtained  from  a  current. 

MANIPULATION. — Set  up  the  apparatus  as  in  Fig.  35. 
Having  a  arranged  as  in  Exp.  4,  suspend  b  above  it,  and 
disconnecting  the  wires  from  the  galvanometer,  connect 

*  Notice  that  as  the  resistance  of  the  galvanometer  coil  B  and 
the  connecting-wires  is  always  the  same,  any  changes  in  the  amount 
of  current  observed  must  be  due  to  changes  in  the  E.  M.  F.  of  the 
induced  current ;  hence  the  conditions  that  seem  to  determine  the 
amount  of  the  current  are  really  those  which  determine  the  E,  M,  F, 


INDUCED   CURRENTS. 


55 


them  with  the  circuit  as  shown,  the  reverser  being  in 
circuit  with  the  lower  magnet  and  b  being  suspended  a 
little  to  one  side  of  a.*  Close  the  circuit  through  b  and 
then  through  a,  and  notice  the  results.  Suddenly  reverse 


FIG.  35. 

the  current  through  a,  and  see  if  by  reversing  at  the 
right  time  you  can  keep  b  swinging.  A  bar-magnet 
arranged  as  in  Exp.  8  may  be  useful. 

QUESTIONS. — 1.  Is  it  possible  to  obtain  motion  from  an 
electric  current?  2.  Would  it  be  possible  to  construct  a 
machine  on  this  principle  which  could  be  used  to  produce 
motion  from  an  electric  current  ?  3.  What  would  be  the 
essential  parts  of  such  a  machine  ? 

A  mechanical  device  for  fulfilling  these  conditions  and 
thus  obtaining  motion  from  electricity  is  called  an  Electric 
Motor. 

*  Two  cells  may  be  used,  or  the  two  coils  may  be  placed  in  paral- 
lel on  one  circuit. 


MENSUEATION. 
NOTES  ON  MEASUREMENT. 

Units  of  Measure. — If  we  wish  to  know  just  how  many 
times  one  body  is  larger  than  another,  that  is,  if  we  wish 
to  make  an  exact  comparison  between  the  two  bodies,  we 
must  ascertain  the  value  of  each  one  in  terms  of  some 
fixed  standard  of  measurement.  Thus,  to  compare  exactly 
the  lengths  of  two  boards,  as  a  preliminary  we  refer  both 
lengths  to  a  fixed  standard  of  length,  and  find  out  how 
many  times  this  standard  is  contained  in  each  of  the 
lengths.  Or,  again,  suppose  we  wish  to  compare  the 
lengths  of  the  two  lines  AB  and  CD,  Fig.  36.  Let  us 


FIG.  36. 

call  the  short  line  cd  the  standard.  We  find  that  AB  is 
equal  to  10  times  cd  and  CD  —  7  cd.  Then  we  know  that 
the  lengths  of  AB  and  CD  are  as  10  to  7.  In  case  cd  is 
not  contained  an  integral  number  of  times  in  AB  and  CD, 
it  must  be  divided  into  known  fractional  parts,  and  the 
lengths  expressed  as  so  many  cd's  plus  so  many  fractions  of 
cd.  In  the  same  way,  if  we  wish  to  compare  volumes,  a 
standard  volume  must  be  employed.  Thus  we  can  find 

56 


NOTE8  ON  MEASUREMENT. 


how  many  times  the  little  cube,  aficdef,  Fig.  37,  is  con- 
tained in  the  two  larger  cubes.  If  it  is  contained  36  times 
in  one  and  8  times  in  another,  we  say  the  volumes  of  the 
larger  cubes  are  as  8  to  36.  As  a  standard  in  comparing 


FIG.  37. 

values  we  refer  to  dollars;  in  lengths,  we  refer  to  feet, 
meters,  or  miles;  in  volumes,  we  refer  to  quarts,  gallons, 
or  cubic  inches,  etc.  Such  a  standard  is  called  a  Unit. 

English  and  French  Systems. — Of  course  any  length  or 
volume  could  be  used  as  a  unit,  but  in  practice  those 
adopted  by  the  government  or  by  custom  are  employed. 
Measurements  of  length,  breadth,  or  thickness  are  called 
Linear  Measurements.  The  common  standard  of  length 
is  the  yard,  which  was  originally  adopted  by  the  English 
Government  as  the  length  of  a  certain  metal  rod  in  their 
possession,  and  has  been  accepted  by  our  own  Government. 
The  smaller  units  are  the  foot  (one  third  of  a  yard),  and  the 
inch  (one  thirty-sixth  of  a  yard,  or  one  twelfth  of  a  foot). 
These  are  called  the  English  units,  and  in  using  them  we 
are  said  to  use  English  Measure.  The  inch  is  commonly 
divided  into  halves,  fourths,  eighths,  sixteenths,  etc.  In 
scientific  work,  however,  fractions  of  an  inch  are  expressed 
as  decimals.  We  also  use  the  French  or  Metric  System. 
Its  standard  is  the  length  of  a  certain  rod,  called  a  Meter, 


58  MENSURATION. 

which  is  in  the  possession  of  the  French  Government. 
This  is  divided  into  100  equal  parts,  called  centimeters, 
and  into  1000  parts,  called  millimeters.  Thus  a  centi- 
meter equals  10  millimeters.  These  prefixes,  cent  and 
mill,  and  their  meanings,  are  familiar  in  our  money. 

Dollar.  Meter.  1. 

Cent.  ^         Centimeter. 
Mill.  Millimeter. 


This  system  has  the  advantage  of  being  divided  decimally, 
so  that  a  change  from  one  unit  to  another  can  be  effected 
by  moving  the  decimal-point. 

As  a  unit  of  Surface,  we  use  a  surface  equal  to  that  of  a 
square  measuring  a  unit  of  length  on  each  side.  Thus  we 
have  a  square  yard,  square  meter,  etc.  Such  measure  is 
called  Surface  or  Square  Measure.  The  surface  expressed 
in  square  measure  is  the  Area. 

For  comparing  volumes,  we  use  a  volume  equal  to  that 
of  a  cube,  measuring  a  unit  of  length  on  each  edge.  Thus 
we  have  a  cubic  foot,  cubic  meter,  etc.  The  unit  used  in 
our  experimental  work  is  generally  the  cubic  centimeter, 
and  sometimes  1000  cu.  cm.  or  a  liter.  We  have  also 
quarts,  gallons,  etc.,  these  quantities  being  the  volumes  of 
certain  vessels  belonging  to  the  Government. 

Change  from  one  System  to  the  Other.  —  If  we  know  the 
value  of  one  unit  in  terms  of  another,  we  can  change  from 
one  system  to  another.  The  meter  is  39.37Ciwches  long. 
Suppose  we  wish  to  express  26  meters  in  yards.  If  one 
meter  =  39.3*&i0.,  26  meters  =  26  X  39.37,  or  1023.62  in., 

1023.62 

and  as  one  yard  =  36  in.,   —  —  —  =  number  of    yards 

oo 

4l  28.85.  Again,  let  us  -change  15  yards  to  meters.  15 
yds.  =  15  X  36  in.  =  540  in.  If  one  meter  =  39.37  in., 
there  will  be  as  many  meters  in  540  in.  as  39.37  is  con- 
tained in  540,  or  13.7  meters.  Another  method  is  as  fol- 


DETERMINATION  Of  LENGTH.  59 

lows:  One  yard  =  36  in.,  one  meter  =  39.37;  then  a  yard 

36  39.37 

—  ^7-^  of  a  meter,  and  a  meter  —  — — -   of  a  yard.     If 


we  change  these  fractions  to   decimals,  we  get   1  yard 

nr»  Oft   OfV 

=  .-Trimeters,  =  0.9144meter;  1  meter  =  -^--  =  1.0936 
39. o7  oo 

yds.  Then  if  1  meter  =  1.0936  yards,  26  meters  will 
equal  26  X  1.0936  yds.,  or  28.85.  Similarly,  if  1  yd. 
=  0.9144  meter,  15  yds.  =  15  X  0.9144  =  13.7  meters. 

Abbreviations. — Meter,  m. ;  centimeter,  cm. ;  millimeter, 
mm. ;  liter,  1. ;  cubic  centimeter,  cu.  cm. 

It  must  be  remembered  that  in  surface  measurement 
the  units  go  by  the  square  of  10,  and  in  cubic  measure  by 
the  cube  of  10.  Thus  there  are  100'  or  10,000  sq.  cm.  in 
1  sq.  m.,  and  1003  or  1,000,000  cu.  cm.  in  a  cu.  m. 

DETERMINATION   OF  LENGTH. 

Scales. — The  English  Scale  gives  results  in  inches,  and 
is  shown  as  commonly  arranged  in  Fig.  38.  The  long 
numbered  lines 
mark  inches;  the 
shorter  lines,  half- 
inches ;  the  still 
shorter,  quarter- 
inches  ;  and  the 
shortest,  eighths.  FIG.  38. 

The  results  are  here  expressed  in  inches  and  decimals  of 
an  inch,  not  in  vulgar  fractions;  as  0.125,  instead  of  £, 
or  2.375  in.  for  2|  in.  Yard-sticks  are  used  in  laboratories.* 

The  usual  form  of  the  Metric  Scale  is  shown  in  Fig.  39. 
The  long  lines,  as  aa,  mark  decimeters;  the  shorter  num- 
bered lines,  as  bb,  centimeters;  the  still  shorter,  cc,  0.5  cm., 
or  5  millimeters;  the  shortest  lines,  millimeters.  Readings 

*  In  some  forms  of  meter-sticks  there  is  an  inch-scale  on  one  side. 
Do  not  use  these  for  yard-sticks. 


{ 


60 


MENSURATION. 


are  usually  expressed  in  centimeters  arid  decimals  of  a  cen- 
timeter. For  example,  the  scale  to  the  line  AB  reads,  in 
Fig.  39  (from  right  to  left),  59  cm.  plus  3  mm. ;  this  would 
be  recorded  59.30  cm.  Meters  are 
used  for  distances  of  over  100  cm. 
When  the  figures  on  scales  are  right 
side  up,  the  scale  reads  from  right  to 
left.  This  must  be  remembered  or 
mistakes  will  happen,  as  it  is  natural 
to  try  to  read  from  left  to  right. 
Tenths  of  millimeters  should  be  esti- 
mated by  the  eye. 

Reading  Scales. — The  scales  are  car- 
ried out  to  the  edge  of  the  rod  (Figs. 
40  and  41),  and  when  possible  this 
os  edge  should  be  placed  against  the  dis- 
cs tance  to  be  measured,  as  in  Fig.  40, 
ta  where  it  is  desired  to  measure  the  dis- 
tance between  the  lines  aa.  Where 
the  scale  cannot  be  applied  directly  to 
the  object,  be  sure  that  the  line  of  sight 
is  always  perpendicular  to  the  scale. 
A  metric  scale  should  be  read  to  TV 
mm.,  the  fraction  of  a  millimeter  di- 
vision being  estimated  by  the  eye.  In 
general,  an  attempt  should  be  made 
to  read  a  scale  to  a  fraction  of  the 
smallest  division. 

When  determining  shorter  distances 
than  the  length  of  the  measuring  rod, 
where  the  body  is  loose  and  can  be  brought  directly 
against  the  scale,  it  is  not  best  to  start  at  one  end  of  the 
rod,  but  rather  to  bring  the  body  to  be  measured  near 
the  middle  of  the  rod,  place  one  point  on  a  numbered 
line  (in  a  metric  scale  one  of  the  decimeter  lines),  and 


^-z 


DETERMINATION  OF  LENGTH. 


61 


read  the  position  of  each  point  on  the  scale.  Suppose, 
for  example,  it  is  desired  to  measure  the  length  of  the  box 
A  BCD  in  Fig.  41.  Lay  the  scale  down  on  top  as  in  the 
the  diagram,  and  read  the  positions  of  A  and  B.  Say 
A  =  26.14  cm.,  B  —  42.81  cm.,  then  B  —  A  =  42.81  — 
26.14,  or  16.67  cm. 


FIG.  40. 

Suppose,  again,  the  diameter  of  a  sphere  is  needed. 
Obtain  two  rectangular  blocks,  aa  in  Fig.  42,  and  place 
the  sphere  between  them,  the  whole  resting  on  a  level 
surface.  Bring  the  blocks  up  against  the  sphere  with  their 
faces  parallel.  Then  the  distance  between  the  blocks  is  the 
diameter  of  the  sphere.  Measure  from  edge  to  edge  di- 


FIG.  41. 

rectly  over  the  centre  of  the  sphere.  The  ball  should  be 
turned  and  the  work  repeated  a  few  times.  Both  blocks 
should  be  set  against  a  smooth  vertical  surface.  In  all 
these  cases  the  same  precaution  is  necessary, — to  have  the 
line  of  sight  at  right  angles  to  the  surface  on  which  the 
scale  is  marked. 


62  MENSURATION. 

When  the  scale  cannot  be  brought  up  to  the  body,  special 
methods  are  resorted  to.  One  is  called  The  Compass 
Method.  A  pair  of  compasses  or  dividers  are  adjusted 

until  the  distance  between 
their  points  is  just  that  to 
be  measured.  The  compasses 
are  then  applied  to  the  scale, 
with  one  point  on  a  num- 
bered line,  and  the  position 
of  the  other  point  is  read. 
Sometimes  a  pointer  is  to  be  read  against  a  scale,  as  in 
getting  the  Coefficient  of  Expansion.  Always  have  the 
pointer  as  near  the  scale  as  possible,  but  not  touching  it, 
and  arranged  so  that  in  moving  it  along  the  scale  it  is  the 
same  distance  from  it.  Always  read  from  the  same  side  of 
the  pointer.  Best  of  all,  end  the  pointer  with  a  fine  needle, 
and  have  the  point  of  the  needle  read  on  the  scale.  A 
magnifying-glass  is  often  of  assistance. 


FIG.  42. 


EXERCISE   1. 

PRACTICE  IN  THE  USE  OF  LINEAR  SCALES. 

EXPERIMENT. 

Apparatus.—  A  sheet  of  paper  on  which  two  crosses  have  been 
ruled  with  a  sharp  pencil,  30  or  40  cm.  apart;  a  meter-stick  with 
English  scale  on  one  side  (or  a  meter-stick  and  a  yard-stick). 

OBJECT. — To  determine:  (a)  The  distance  between  the 
centres  of  the  two  crosses  in  inches,  (b)  The  same  distance 
in  centimeters,  (c)  From  these  data,*  the  number  of 
inches  in  a  meter. 

MANIPULATION. — Lay  the  sheet  of  paper  smoothly  upon 
the  table,  place  the  metric  scale  upon  it,  bring  the  centres 
of  both  crosses  to  the  edge  of  the  scale,  and  record  their 


*This  word  means  the  numerical  results  of  the  experiment,  which 
are  afterwards  used  in  the  calculation. 


PRACTICE  IN  THE  TTSE  OF  LINEAR  SCALES.      63 


readings.  Read  the  scale  to  0.1  mm.,  observing  all  the  pre- 
cautions given  in  the  "  Notes  on  Measurement."  Try  five 
times,  using  different  parts  of  the  scale  each  time.  Record 
results  as  in  the  following  example,  which  gives  the  actual 
data  of  one  set  of  determinations  with  this  apparatus : 

TABLE  I.— METRIC  MEASURE. 


No.  of  Trial. 

Reading  L.  H.  Point. 

Reading  R.  H.  Point. 

Length  in  Cm. 

1 

72.81  cm. 

50.00  cm. 

22.81 

2 

82.80    " 

60.00    " 

22.80 

3 

51.79    " 

29.00    " 

22.79 

4 

61.30    " 

38.50    " 

22.80 

5 

30.79    " 

8.00    " 

22.79 

Average  length  in  cm.,  22.79  cm. 

With  the  same  precations,  measure  the  distance  between 
the  centres  of  the  crosses  in  the  English  system,  reading  to 
one-sixteenth  (0.0625)  inch,  mentally  changing  the  fractions 
of  an  inch  to  decimals.  Arrange  the  results  as  follows : 

TABLE  II.— ENGLISH  MEASURE. 


No.  of  Trials. 

Reading  L.  H.  Point. 

Reading  R.  H.  Point. 

Length  in  Inches. 

1 

1  inch. 

9.937  inches. 

8.937 

2 

5  inches. 

13.975      " 

8.975 

3 

7      " 

15.959      " 

8.959 

4 

10      " 

18.968      " 

8.968 

5 

13      " 

21.975      " 

8.975 

Average  length  in  inches,  8.963  inches. 

CALCULATION. — Having  now  the  values  of  the  same  dis- 
tance in  centimeters  and  in  inches,  the  number  of  centi- 
meters to  the  inch  can  be  found  by  the  following  calcula- 
tion: 

Number  of  cms.  :  100  cms.  : :  number  of  inches  :  x. 
x  =  number  of  inches  in  100  cms.  (1  meter). 


64  MENSURATION. 

Taking  the  data  given  above  : 

22.79  cms.  :  100  cms.  ::  8.963  inches  :  x 
_100  X  8.963 

~  39'31 


which  would  be  the  value  given  by  these  data  for  the  num- 
ber of  inches  in  the  meter.* 


EXERCISE  2. 

THE  RELATION  OF  CIRCUMFERENCE  TO  DIAMETER. 
EXPERIMENT. 

Apparatus.—  Meter-stick  (English  and  French  scales),  card-board 
circles,  10  cm.,  20  cm.,  and  30  cm.  in  diameter;  pencil;  strip  of  paper 
or  card-board  about  1  m.  long. 

OBJECT. — To  obtain  answers  to  the  following  questions  : 
(1)  Is  there  any  definite  relation  between  the  diameter  of 
a  circle  and  its  circumference  ?  (2)  Do  these  results  hold 
true  for  more  than  one  method  of  measurement  ?  (3)  Is 
this  relation  the  same  for  circles  of  different  diameters? 
(4)  Given  the  diameter  of  a  circle,  can  the  circumference 
be  found  ?  If  so,  how  ?  (5)  Given  the  circumference  of 
a  circle,  can  the  diameter  be  found  ?  If  so,  how  ?  f 

MANIPULATION". — Method  A.  Make  a  pencil-mark  on 
the  edge  of  the  circular  disk  of  paper  (Fig.  43).  Roll  the 

disk  along  a  straight 
line  ruled  on  a  piece 
of  paper  tacked  to  the 
table,  starting  with  the 
Fia  4a  pencil-mark  just  on  the 

line,  and  rolling  until  the  mark  just  touches  the  line  again. 

*  These  data  give  a  value  a  little  below  the  true  one,  viz.,  39.37. 
f  As  iu  all  experimental  work,  first  lay  out  a  general  method.     In 
this  case  the  general  method  is, — to  answer  question  1,  measure  the 


RELATION  Off  CIRCUMFERENCE  TO  DIAMETER.     65 

Carefully  measure  the  distance  on  the  line  between  the 
two  points  touched  by  the  pencil-mark.  This  gives  you 
the  circumference. 

Method  B.     Lay  the  measuring-rod  on  the  table  and  roll 
the  disk  along  it,  as  in  Fig.  44.     This  gives  the  required 


n 


FIG.  44. 

length  directly  on  the  rod.  To  measure  the  diameter,  lay 
the  disk  flat  on  the  table  and  measure  the  distance  across 
it  at  its  widest  part.  Make  each  measurement  both  in 
centimetres  and  inches;  repeat  three  times,  and  record  the 
results  each  time.  The  three  numbers  obtained  for  the 
circumference  will  not  be  just  the  same,  owing  to  errors  in 
manipulation,  reading,  etc.  Add  them,  and  divide  the 
sum  by  the  number  of  measurements.  This  gives  the 
average  measurement  of  the  circumference.*  Do  the  same 
for  the  diameter  measurements.  Then  divide  the  average 
circumference  by  the  average  diameter.  This  gives  a  num- 
ber which,  except  for  errors,  is  that  by  which  the  diameter 
must  be  multiplied  to  obtain  the  circumference.  It  should 
be  a  little  over  three,  and  should  be  carried  out  to  four 
decimal  places.  Do  the  same  for  the  measurements  in 
inches,  and  compare  the  numbers  obtained  in  the  two 


circumference  and  diameter  of  a  circle  and  find  if  any  relation 
exists  between  them  ;  to  answer  questions  4  and  5,  use  the  knowl- 
edge obtained  in  answering  question  1  ;  to  answer  question  2,  com- 
pare results  obtained  by  using  different  methods  of  measurement  ; 
to  answer  question  3,  use  circles  of  different  sizes. 

*  Of  course  this  is  to  be  done  separately  for  the  measurements  in 
inches  and  in  centimeters. 


66 


MENSURATION. 


cases.      Arrange  in  the  note-book  a  table  of   results  as 
follows  : 


CIRCLE  I. 

Measured  in  centimeters.    Method  * « A. ' 


Circum. 

Diana. 

Av.  Circum. 

Av.  Diana. 

Av.  Circum. 

Av.  Diam. 

CIRCLE  I. 
Measured  in  inches.    Method  "  B.' 


Circum. 

Diam. 

Av.  Circum. 

Av.  Diam. 

Av.  Circum. 

Av.  Diam. 

Kepeat  in  exactly  the  same  way  with  Circle  II.  Answer 
in  order  the  questions  given  above,  and  also  state  which 
method  in  your  opinion  yields  the  best  results,  and  why  ? 

CALCULATION. — There  have  now  been  obtained  at  least 
four  values  for  the  number  which  stands  for  the  numerical 
relation  between  diameter  and  circumference.  Average 
them,  and  the  result  should  be  nearly  correct.  Using  this 
number,  solve  the  following: 

PROBLEMS. — 1.  A  circle  has  a  diameter  of  6  cm.;  find 
the  circumference.  2.  If  the  circumference  is  25  cm., 
find  the  diameter.  3.  If  the  diameter  is  6  inches,  find  the 
circumference.  4.  If  the  circumference  is  25  inches,  find 
the  diameter.  The  number  is  represented  in  geometry  by 
the  sign  it  (pronounced  "  pi ").  Then,  with  this  sign,  using 
D  as  the  symbol  for  the  diameter  and  C  for  the  circumfer- 
ence, express  as  an  algebraic  equation  the  rule  for  solving 
such  problems  as  the  above. 


DETERMINATION  OF  VOLUMES. 


67 


-50 


DETERMINATION  OF  VOLUMES. 

The  Graduate  Cylinder.— There  are  two  kinds  of  meas- 
uring vessels  in  use  for  fluids — those  measuring  only  a  fixed 
quantity  and  those  meas- 
uring varying  quantities. 
Of  the  latter  kind,  the 
two  commonly  used  in 
laboratory  work  are  grad- 
uated cylinders  and  bu- 
rettes. The  graduated 
cylinder,  often  called 
simply  a  graduate,  is  a 
glass  cylinder  furnished 
with  a  foot  so  as  to  stand 
upright,  and  with  a  scale  20- 

for  reading  volumes,  usu- 
ally in  cubic  centimeters. 
The  scale  is  engraved  on 
the  glass,  and  arranged  as 
in  Fig.  45.  There  is  a 
long  numbered  line  for 
every  10  cu.  cm.,  as  a  a. 
Between  these  are  shorter 
lines,  marking  cubic  centi- 
meters, as  c  c;  and  between 
these,  in  turn,  still  shorter 
ones,  marking  half  cu.  cm. 
Such  a  scale  is  said  to  read 
to  0.5  c.c.  There  are  usu- 
ally two  scales,  one  having 
the  0  at  the  top  and  the  FIG.  45. 

other  at  the  bottom,  the  former  used  in  measuring  the 
volumes  of  liquids  poured  out  of  the  cylinder,  the  latter 
in  measuring  the  volumes  of  liquids  poured  in. 


-10 


68 


MENSURATION. 


On  looking  horizontally  at  a  graduate    containing  a 
liquid,  the  surface  of  the  liquid  appears  as  a  dark  band, 


FIG.  46. 


FIG.  47. 


usually  curving  down  in  the  centre,  as  in  Fig.  46.  This 
curve  is  called  the  meniscus,  and  the  line  correspond- 
ing to  the  loivest  point  of  the  meniscus  is  taken  as  the 
level  of  the  liquid.  The  cylinder  must  be  placed  on  a 
firm  horizontal  surface,  and  the  eye  brought  to  the  level 
of  the  meniscus  and  directly  opposite  the  scale.  In  Fig. 
47  a  represents  the  correct  method  of  reading,  b  and  c 
the  incorrect,  b  would  give  a  reading  greater  and  c  less 
than  the  true  one.  Errors  caused  by  failure  to  read  a 
scale  with  the  line  of  sight  in  the  proper  position  are  said 
to  be  due  to  Parallax.  The  following  method  will  avoid 
such  errors: 

Take  a  piece  of  stiff  paper  about  1J  X  4  inches,  being 
sure  that  the  upper  edge  is  clean  and  straight.  Wrap  it 
around  the  cylinder,  and  allow  a  portion  to  project,  as 
shown  in  Fig.  48.  Grasp  the  projecting  portion  with  the 
finger  and  thumb,  taking  care  that  the  upper  and  lower 


DETERMINATION  OF  VOLUMES. 


69 


edges  are  even  with  each  other.  Draw  the  paper  tightly 
around  the  cylinder,  and  move  it  until,  on  sighting  across 
the  top  edge  from  one  side  to  the  other,  the  meniscus  just 


FIG.  48. 


FIG.  49. 


touches  it;  Fig.  49.  In  this  position  the  "sight "  is  horizontal. 
If  the  upper  edge  of  the  paper  is  just  on  a  line  of  the 
scale,  this  gives  the  reading  ;  but  if  not,  the  fraction  must 
be  estimated  by  the  eye  and  expressed  as  a  decimal.  Sup- 
pose it  comes,  as  in  Fig.  50,  between  the  17  and  18  line.  If 
half-way  between,  read  17.5 ;  if  one  third  the  way,  17.33  ; 
if  two  thirds,  17.66  ;  if  three  fourths,  17.75;  etc.  On  the 
graduates  commonly  used  remember  that  the  space  between 
two  lines  is  half  a  cubic  centimeter.  Hence,  if  half-way, 
read  0.25  ;  if  one  fourth  above,  0.12  cu.  cm.;  etc.  As  a 


70 


MENSURATION. 


rule,  any  scale  can  be  read  to  one   tenth  of  its  smallest 
division.     When  there  is  occasion  to  read  mercury  in  a 


FIG.  50. 


tube  or  graduate,  it  will  be  found  that  the  meniscus  is  re- 
versed (Fig.  51),  curving  up  in  the  centre  instead  of  down. 
In  this  case  always  read  the  level  of  the  top  of  the  menis- 
cus, which  can  be  done  by  the  method  just  described. 

When  measuring  out  from  a  cylinder,  it  is  generally 
best  to  fill  it  first  to  the  0  mark;  though  of  course  the 
level  of  the  liquid  can  be  read  anywhere  on  the  scale,  and 
then  read  again  after  pouring  off;  the  difference  in  the 
readings  giving  the  volume  poured  off.  In  pouring  from  a 
cylinder,  spilling  can  be  avoided  by  holding  one  end  of 
a  glass  rod  against  the  lip  of  the  jar,  and  the  other  end 


DETERMINATION  OF  VOLUMES. 


71 


against  the  inside  of  the  receiving  vessel,  as  in  Fig.  52.    The 
liquid   will   follow  the  rod.      On  righting  the  cylinder 


FIG.  51. 


FIG.  52. 


always  wait  a  moment  before  reading  the  volume,  so  that 
the  water  which  has  collected  on  the  sides  may  run  back 
again. 

The  Burette. — This  is  a  long  narrow  tube  having  a  scale 
on  one  side.  (See  Fig.  53.)  A  rubber  tube  is  drawn  over 
the  lower  end,  which  is  narrowed,  and  the  tube  is  provided 
with  a  spring  clamp,  a,  which  pinches  the  sides  together. 
On  pressing  the  ends  of  the  clarnp  the  rubber  tube  is 
allowed  to  expand  and  the  liquid  runs  out  at  C  at  a  rate 
proportioned  to  the  pressure  on  the  clamp.  A  burette  is 
filled  from  the  top  and  usually  supported  in  a  vertical  posi- 
tion by  a  clamp.  Burettes  are  usually  graduated  as  in  Fig. 
54,  which  shows  a  portion  of  the  scale.  The  long  lines 
mark  cu.  cm.  Each  space  between  the  cu.  cm.  lines  is 
divided  into  five  parts.  Thus  the  scale  reads  to  one  fifth 
(0.2)  cu.  cm.  The  lines  are  numbered  at  every  two  cubic 
centimeters.  In  estimating  fractions,  one  half  a  space 
=  0.1  cu.  cm.,  one  third  =  0.06,  two  thirds  =  0.12  cu.  cm., 
etc.  The  scale  may  be  read  with  a  piece  of  paper  like  a 
graduated  cylinder. 


72  MENSURATION. 

Many  burettes  are  provided  with  a  float,  consisting  of 
a  bulb  of  glass  shaped  as  in  Fig.  55,  with  a  little  mercury 
in  the  lower  end  so  that  it  will  float  upright.  A  line  is 
ruled  around  it  (a  in  Fig.  55).  When  the  float  is  placed  in 
the  burette  it  floats  in  the  liquid,  rising  and  falling  with 
it,  and  the  line  is  observed  on  the  scale  through  the  glass. 
The  position  of  the  line  is  read  as  the  level  of  the  liquid. 
As  the  float  is  of  nearly  the  same  diameter  as  the  inside  of 
the  burette  (thus  bringing  the  line  very  near  the  scale), 
with  ordinary  care  there  is  little  danger  of  error  due  to 
parallax.  It  is  well  to  tap  the  burette  gently  before  read- 
ing, as  the  float  is  apt  to  stick  a  little  to  its  sides.  When 
filling  the  burette,  pour  the  liquid  in  until  the  line  mark- 
ing its  level  is  above  the  0  mark,  which  is  near  the  top  of 
the  scale,  and  carefully  draw  out  the  excess  until  the  read- 
ing is  0,  allowing  the  waste  liquid  to  run  into  a  vessel  pro- 
vided for  the  purpose.  To  make  sure  that  no  air  remains 
in  the  rubber  tube,  fill  the  burette  part  full,  place  the 
upper  end  in  the  mouth,  and,  holding  the  clamp  open, 
blow  the  liquid  nearly  out.  This  repeated  several  times 
will  generally  drive  out  the  air. 

Instead  of  a  clamp,  burettes  are  sometimes  provided  with 
the  arrangement  shown  in  Fig.  56.  A  piece  of  glass  rod 
about  a  fourth  of  an  inch  long,  whose  diameter  is  such 
that  it  will  fit  tightly  in  the  rubber  tube,  is  cut  off,  and  the 
ends  are  rounded  by  heating.  The  little  plug  thus  formed 
is  thrust  about  half-way  up  the  tube.  By  pinching  with 
the  forefinger  and  thumb  on  one  side  of  the  tube  at  the 
point  where  the  plug  is  situated,  a  channel  is  formed 
through  which  the  liquid  can  pass.  The  rate  at  which  the 
liquid  flows  depends  upon  the  amount  of  the  pressure. 

Graduated  Flask. — This  is  a  vessel  having  a  mark  en- 
graved upon  its  neck.  When  filled  so  that  the  lower  end 
of  the  meniscus  just  touches  the  mark,  the  flask  holds  a 
fixed  quantity  of  liquid.  Those  commonly  used  hold  1 


DETERMINATION  OF  VOLUMES. 


73 


c  c 


FIG,  53, 


FIG.  54. 


A 


74  MENSURATION. 

liter  (1000  cu.  cm.),  one-half  liter  (500  cu.  cm.),  and 
one-fourth  liter  (250  cu.  cm.),  their  capacity  being  marked 
upon  them.  For  accurate  measurements,  fill  the  flask 
nearly  to  the  mark,  and  placing  the  eye  so  that  the  mark 
appears  as  a  straight  line,  drop  in  the  liquid  with  a  piece 
of  glass  tube  *  until  the  correct  level  is  reached.  If  you  fill 
above  the  mark,  use  the  tube  to  withdraw  some  of  the 
liquid.  The  flask  should  rest  on  a  firm  horizontal  surface. 
It  is  well  to  mark  the  position  of  the  line  by  a  piece  of 
paper,  as  described  in  the  directions  for  using  graduates. 

EXERCISE  3. 

PRACTICE  IN  DETERMINING  VOLUMES. 

EXPERIMENT. 

Apparatus.—  Method  A:  Graduated  cylinder;  body  whose  volume 
is  to  be  measured;  water. 

Method  B:  Piece  of  fine  wire;  cylinder;  rubber  band;  paper  for 
markers;  body;  water. 

Method  C:  Burette  or  equivalent;  ungraduated  jar  or  equivalent; 
rubber  band;  paper  for  markers ;  body;  water. 

OBJECT, — To  determine  the  volume  of  an  irregular  body 
by  displacement. 

MANIPULATION. — Method  A.  Fill  the  graduated  cylin- 
der part  full  of  water,  read  the  volume  (as  a  in  Fig.  57), 
observing  all  the  precautions  given  in  the  preliminary 
notes  on  determination  of  volume,  and  record  the  reading. 
Drop  the  body  whose  volume  is  to  be  determined  (as  e)  into 
the  cylinder,  and  again  read  the  volume  (as  C).  The  dif- 
ference in  the  readings  on  the  scale  (a  to  C)  is  the  volume 
of  the  body. 

Method  B.  Attach  a  fine  thread  or  wire  to  the  body 
whose  volume  is  to  be  determined,  and  drop  the  body  into 
the  glass  cylinder.  Partially  fill  the  cylinder  with  water. 

*  As  in  using  the  sliejl^c  in  tke  exercise  oij  the  lines  of  magnetic 
forge, 


PRACTtC!fi  IN  DETERMINING   VOLUMES. 


FIG.  57. 


Mark  the  level  of  the  water  by  means  of  a  piece  of  paper 
about  4  cm.  wide  and  long  enough 
to  be  wrapped  several  times  around 
the  cylinder.  Fasten  this  marker 
in  position  by  a  rubber  band.  Be 
sure  that  the  upper  edge  of  the 
paper  is  at  the  same  level  all 
around  the  cylinder,  and  that,  when 
looked  at  horizontally,  the  line  of 
the  paper  just  touches  the  lowest 
point  of  the  meniscus.  By  means 
of  the  thread  remove  the  object, 
allowing  as  much  of  the  water  as 
possible  to  drain  back  into  the 
cylinder.  Run  in  water  with  a 
burette  until  the  level  in  the  cylin- 
der is  the  same  as  before.  The 
volume  of  water  run  in,  as  measured 
on  the  burette,  is  the  volume  of  the  body. 

Method  C.  From  a  burette,  run  into  a  dry,  empty 
cylinder  any  known  volume  of  water, — say  50  cu.  cm. 
— and  mark  its  meniscus  by  a  strip  of  paper  as  in  B. 
Empty  the  cylinder,  wipe  it  dry  and  put  in  the  object 
whose  volume  is  to  be  determined.  Run  in  water  from 
the  burette  until  the  level  is  the  same  as  it  was  before; 
note  the  reading  of  the  burette.  The  difference  between 
the  two  volumes  of  water  drawn  from  the  burette  is  the 
volume  of  the  object.  For  an  object  that  floats,  a  sinker 
must  be  used.  First  get  the  volume  of  the  sinker  alone, 
attach  the  object  to  it,  and  get  the  volume  of  both  ;  then 
by  subtracting  the  volume  of  the  sinker  from  the  volume  of 
the  two,  the  volume  of  the  body  alone  can  be  obtained. 

Determine  by  each  of  these  methods  the  volume  of  the 
same  body.  Compare  the  results,  and  state  which  is  the 
best  process  in  your  opinion,  and  why.  As  many  deter- 


76  MENSURATION 

minations  should  be  made  as  time  allows,  and  the  results 
averaged.     Arrange  as  follows  : 

METHOD  A.  1st  Trial.  2d  Trial. 

Vol.  water  plus  body  =                   cu.  cm.  cu.  cm. 

"     alone  =                    "     "  "      " 

"    of  body  —                     "     "  "     " 

Average  vol.  by  A  =  cu.  cm. 

METHOD  B.  1st  Trial.  2d  Trial. 

Burette-reading  after  running  in,  cu.  cm.  cu.  cm. 

before    "  "     "  "      " 


Difference  in  burette-reading, 

or  volume,  "     "  "      " 

Average  vol.  by  B  =  cu.  cm. 

METHOD  C.  1st  Trial :  Body  out.      2d  Trial. 

Burette  reading  after  running  in,  cu.  cm.  cu.  cm. 

"  "       before    "          "  "      "  ••      " 


Volume  run  in,  "      "  "      " 

Body  in. 

Burette-reading  after  running  in,  cu.  cm.  cu.  cm. 

before    "          "  •  "      "  "      " 


Vol.  run  in. 

Vol.  run  into  empty  cyl.,  cu.  cm.  cu.  cm. 

"      "      "    cyl.  +body,  "     "  •*     " 


"    of  body, 
Av.  vol.  of  body  =  cu.  cm. 

EXERCISE  4. 

CROSS-SECTION  AND  INTERNAL  DIAMETER  OF  A  TUBE. 

EXPERIMENT. 

Apparatus.— Glass  tube;  burette  or  equivalent;  markers;  rubber 
band;  cork;  water;  meter-stick. 

OBJECT. — To  find  the  cross-section  and  internal  diameter 
of  a  tube  by  determining  its  length  and  volume. 


CROSS-SECTION  AND  DIAMETER  OF  A  TtTBE.      T? 

MANIPULATION. — Method  A.  Cork  one  end  of  the  tube, 
and  pour  in  water  enough  to  cover  the  cork  to  a  depth  of 
about  1  cm.  Carefully  mark  the  level  of  the 
water  by  means  of  a  piece  of  paper  and  rubber 
band,  as  in  the  preceding  experiment.  Run  in 
a  known  volume  of  water,  say  40  or  50  cu.  cm. 
Place  on  your  tube  a  second  measuring-paper, 
and  move  the  paper  until  it  just  marks  the  level 
of  the  liquid  when  the  tube  is  held  vertically. 
The  distance  between  the  two  water-levels,  as 
indicated  by  the  markers,  is  the  height  to  which 
the  known  volume  has  filled  the  tube.  Pour  out 
the  water  and  place  the  tube  close  against  the 
meter-rod,  taking  care  not  to  disturb  the  mark- 
ers. Record  the  distance  corresponding  to  ab 
in  Fig.  58.  Then 

Volume 


Cross-section  = 


Height* 
Repeat  several  times  with  varying  volumes. 


Fro.  58. 

This  will  re- 
duce the  errors  due  to  the  uneven  bore  of  the  tube.  Ar- 
range the  results  as  follows  : 


No.  Trial. 

Vol.  run  in. 

Height  in  Tube. 

Cross-section. 

Average  cross-section  = 

Method  B.  Place  the  two  paper  markers  so  that  they 
are  a  certain  distance  apart  *  from  upper  edge  to  upper 
edge,  as  measured  on  the  scale.  Set  the  tube  upright 
and  run  in  water  until  the  level  of  the  liquid  is  just  at  the 
lower  mark.  Read  the  burette.  Run  in  more  water  to 


*  The  distance  between  the  markers  should  be  an  integral  number 
on  the  scale. 


78  MENSURATION. 

the  level  of  the  upper  mark,  and  read  the  burette  again. 
The  difference  of  the  readings  is  the  volume  run  in  be- 
tween the  markers.  Repeat  several  times  with  the  markers 
at  various  heights.  Arrange  results  on  the  plan  indicated 
in  the  preceding  exercise.  In  Method  A,  the  volume  being 
measured  to  an  integral  number,  the  chief  liability  to  error 
is  in  the  determination  of  the  height.  In  Method  B,  the 
height  being  measured  to  an  integral  number,  the  chief 
liability  to  error  is  in  the  determination  of  the  volume. 
Therefore  the  values  obtained  by  averaging  the  results  of 
the  two  methods  should  be  very  nearly  correct. 

To  find  the  diameter,  take  the  average  value  for  the  cross- 

Z>2 

section  and  substitute  it  for  A  in  the  formula,  A  —  n—  . 

4 

Determine  the  cross-section  of  a  glass  tube  by  both  meth- 
ods, and,  if  so  instructed,  compute  its  diameter,  calculating 
the  internal  diameter  by  this  formula;  carefully  measure  it 
according  to  notes  on  Measurement,  and  compare  the  cal- 
culated and  the  measured  results.  For  comparison,  take 
the  average  of  the  diameters  of  the  two  ends  of  the  tube. 
All  measurements  of  length  should  be  made  to  0.1  mm., 
and  burette-readings  to  0.1  cu.  cm.  All  values  of  cross- 
sections  to  be  expressed  in  sq.  cm.,  and  carried  out  to  fourth 
decimal  place.  Express  the  values  of  diameters  in  mm.  to 
first  decimal  place. 

DETERMINATION  OF  WEIGHT. 

Introductory. — For  exact  comparisons  of  weights,  units 
are  required,  as  in  comparisons  of  lengths  or  volumes. 
The  ordinary  English  units  are  the  pound  (lb.),  and  the 
ounce  (oz.),  one  sixteenth  of  a  pound.  The  pound  is  a 
weight  equal  to  that  of  a  piece  of  metal  in  the  posses- 
sion of  the  government.  The  metric  unit  of  weight  is 
the  gram  (g.  or  grm.),  and  is  the  weight  of  a  cubic  centi- 


DETERMINATION  Off  WElGBT.  79 

meter  of  water  at  a  specified  temperature.  A  larger  unit, 
the  kilogram  (k.),  is  the  weight  of  1000  grams.  The 
gram  is  divided  into  decigrams  (d.  or  dg.),  .1  gram  ;  centi- 
grams (eg.),  .01  gram  ;  milligrams  (mg.),  .001  gram.  Large 
weights  are  expressed  in  kilograms  and  decimals  of  a  kilo- 
gram ;  small  weights  in  grams  and  decimals  of  a  gram. 
In  a  general  way,  the  kilogram,  is  used  in  place  of  the  pound 
in  English  measure,  and  the  gram  in  place  of  the  ounce. 

The  Balance. — This  instrument  is  represented  in  Fig.  59. 
S  is  the  support,  BB  the  beam,  and  PP  the  pans.  Before 
use  the  beam  should  be  level,  and  the  bottoms  of  the  pans 
about  half  an  inch  from  some  surface  underneath.  The  body 
to  be  weighed  should  be  placed  in  the  left-hand  pan,  and 


FIG.  59. 

weights  in  the  right-hand  pan,  one  by  one,  until  the  beam 
again  hangs  level.  Then  the  sum  of  the  weights  used  is 
the  weight  of  the  body.  The  weights  used  in  laboratories 
are  generally  metric.  The  larger  ones  down  to  one  gram 
are  made  of  brass  (Fig.  60),  and  their  values  are  stamped 
on  the  top.  Weights  of  less  than  one  gram  are  made  of 
platinum  or  aluminium.  These  have  values  stamped  on 
them  in  decimals  of  a  gram.*  For  example,  a  weight 
marked  0.1  would  be  0.1  (one  tenth)  of  a  gram,  or  a  deci- 


*  Sometimes  the  smaller  weights  are  made  of  wire.  The  number 
of  parts  represented  is  indicated  by  bending  the  wire  into  a  polygon 
of  a  corresponding  number  of  sides. 


BO  MENSURATION. 

gram;  0.02  means  two  centigrams,  etc.  The  larger  weights 
are  kept  in  holes  bored  in  a  bloc'k  of  wood;  the  smaller 
are  either  in  one  hole  provided  with  a  cover,  or  in  shallow 
holes  covered  by  a  glass  plate.  In  case  the  smaller  weights 


FIG. 


are  in  one  hole,  they  should  be  taken  out  and  placed  upon 
a  piece  of  paper,  marked  as  follows : 

.5  .2  .2  .1 

.05  .02          .02  .01 

Each  weight  should  be  laid  so  as  to  cover  the  mark  cor- 
responding to  it,  and,  except  when  in  the  scale-pan,  should 
be  kept  there  until  the  operation  is  completed.  A  glance 
at  the  uncovered  numbers  on  the  card  then  tells  which 
weights  are  in  the  scale  pan.  Unless  very  heavy  (say  above 
500  grams),  weights  should  be  handled  with  the  pincers 
provided  for  this  purpose,  and  not  with  the  fingers.  All 
weights  should  be  placed  at  once  in  the  proper  receptacle 
when  removed  from  the  scale-pan,  and  never  allowed  to  lie 
on  the  table.  The  large  brass  weights  are  handled  by  the 
knob  on  top.  Never  allow  the  scales  or  weights  to  come  in 
contact  with  anything  that  might  corrode  or  injure  them. 

Weights  are  of  the  following  numbers  and  denominations: 
one  five,  two  twos,  and  a  one.  Thus,  the  weights  under  one 
gram  would  be  one-half  gram  (0.5  grm.),  two  one-fifth 
gram  (0.2  grm.),  and  one  one-tenth  gram  (0.1  grm.).  Or 
there  are  one  100-grm.,  one  50-grm.,  two  20-grm.,  and  one 
10-grm.,  etc. 

Time  is  saved  by  weighing  in  a  methodical  manner,  and 
not  taking  weights  at  random.  Usually  the  weight  of  a 
bodv  can  be  estimated  in  round  numbers,  and  the  first 


^TERMINATION  Of  WEIGHT.  81 

Weight  tried  should  be  about  that  estimated.  For  example, 
the  body  is  estimated  to  weigh  about  20  grm.  Placing  it 
in  the  left-hand  pan,  put  a  20-grm.  weight  in  the  other. 
The  weight-pan  remains  in  the  air,  hence  20  grm.  is  not 
enough.  Add  10  grm.  more:  this  is  too  much.  Replace  by 
5  grm. :  also  too  much.  Replace  by  2  grm. :  now  it  is  too 
little.  Add  2  grm.:  too  little  still.  The  weight  must  be 
between  24  and  25  grm.  Add  0.5  grm. :  too  little.  Add  0.2 
grm.  more:  too  much.  Replace  by  0.1  grm. :  still  too  little. 
Add  0.05  grm.,  and  the  correct  weight  is  found.  On  add- 
ing up  the  weights  in  the  scale-pan  they  amount  to 

24.00  g 

6  dc.  or      .60  g. 
5  eg.  or     .05  g. 

24.65  g. 

Weights  are  usually  expressed  in.grams  and  decimals  of  a 
gram.  We  would  not  say  that  a  weight  was  24  grams,  6 
decigrams,  and  5  centigrams,  but  24.65  grams;  just  as  we 
do  not  say  that  a  thing  cost  2  dollars,  4  dimes,  and  7  cents, 
but  $2.47. 

In  getting  the  weight  of  a  liquid,  one  method  is  to  first 
weigh  the  empty  vessel,  and  then  the  liquid  and  vessel  to- 
gether. For  example,  suppose  10  grams  of  a  liquid  are 
wanted.  Weigh  a  vessel  and  then  add  10  grm.  to  the 
weights  on  the  pan  and  pour  the  liquid  into  the  vessel  until 
the  beam  balances.  Arrange  notes  as  follows,  always  plac- 
ing the  weight  of  the  dish  alone  on  the  lower  line,  since  it 
is  to  be  subtracted  from  the  larger  weight  of  the  dish  and 
liquid : 

Dish  and  liquid  =  26.249 
Dish  alone,          =  16.249 

Liquid  =  10.000 


Another  method,  called  counterpoising,  is  to  place  the 
vessel  in  one  pan,  and  balance  it  by  some  substance,  such 
as  sand  or  shot,  in  the  other.  The  weight  of  the  liquid 
alone  need  not  then  be  determined  by  actual  weighing.  It 
is  generally  easier  to  counterpoise  a  flask  or  dish  than 
to  weigh  it  accurately. 

The  Spring-balance. — In  this,  the  weight  attached  pulls 
out  the  spring  and  registers  itself  by  a  pointer  on  a  scale 
engraved  on  the  brass.  The  scale  is  generally  graduated 
up  to  twenty-five  pounds  and  reads  down  to  one-half  pound, 

A  every  four  pounds  being  numbered.  In  Fig.  61 
the  long  lines  are  pound  marks,  and  the  shorter 
lines  between  them,  half-pound  marks.  In  read- 
ing, be  sure  that  the  eye  is  directly  over  the 
pointer.  Always  read  from  the  same  side  of  the 
pointer,  which  is  usually  wide  enough  to  cover 
half  a  pound  on  the  scale.  The  scale  is  quite 
fine,  and  a  magiiifying-glass  is  often  useful.  As 
the  pointer  is  liable  to  stick,  it  is  well  to  shake 
the  balance  a  little  before  reading.  Be  careful 
to  hold  it  so  that  the  rod  to  which  the  hook  is 
attached  can  slide  freely.  This  is  especially 
needful  when  using  the  balance  to  measure  force. 
FIG.  61.  rp}ie  ba]ance  niust  be  held  just  in  the  line  of  the 
pull;  otherwise  it  will  bind  and  give  incorrect  readings. 
There  are  some  balances  which  read  to  48  pounds.  In 
these  the  scale  only  reads  to  pounds.  After  being  used  to 
reading  on  a  24-pound  balance,  one  is  almost  certain  to 
make  mistakes  in  reading  on  one  of  the  48-pound  bal- 
ances. Balances  reading  up  to  8  oz.  are  also  used.  The 
scale  reads  to  £  oz.  In  using  one  of  these  balances, 
fractions  of  less  than  one  scale-division  should  be  estimated 
by  the  eye.  With  practice  one  should  be  able  to  read  to 
•3*5-  of  an  ounce  (.037  oz.).  Never  leave  a  balance  stretched 
out  any  longer  than  necessary,  as  it  injures  the  spring.  If 


PRACTICE  IN  WEIGHING. 


83 


the  pointer  does  not  stand  at  0  when  there  is  no  pull  on 
the  spring,  read  the  position  of  the  index  before  beginning 
to  weigh,  and  subtract  (if  over  0)  from  subsequent  read- 
ings. Thus,  if  the  pointer  read  one-half  pound,  all  read- 
ings are  half  a  pound  too  high,  and  half  a  pound  must  be 
subtracted.*  A  spring-balance  is  generally  used  to  measure 
forces;  it  is  then  often  called  a  Dynamometer,  i.e.,  "force- 
measurer."  When  a  spring-balance  is  used  for  weighing, 
it  should  never  be  held  in  the  hand,  but  suspended  from 
some  solid  object. 

EXERCISE  5. 

PRACTICE  IN  WEIGHING. 
EXPERIMENT. 

Apparatus,— Scales;  weights;  avoirdupois  weights  or  8-oz.  bal- 
ances (if  the  latter,  one  to  three  students  is  enough).  Several  bodies 
weighing  one  to  two  ounces. 

OBJECT. — To  determine  the  value  of  the  ounce  in  grams. 

MANIPULATION. — Weigh  some  body  to  0.01  grm.  on  the 
scales.f  Determine  the  weight  of  the  same  body  in  ounces 
by  means  of  a  spring-balance  or  by  the  scales  and  English 
weights.  From  the  following  proportion  calculate  the 
number  of  grams  to  the  ounce: 

wt.  in  oz.  :  wt.  1  oz.  ::wt.  in  grins.  :  x. 
x  =  no.  of  grms.  to  the  oz. 

Repeat  with  as  many  different  substances  as  time  allows, 
average  the  values  so  obtained,  and  tabulate  the  results  as 
follows : 


Body. 

Wt.  in  oz. 

Wt.  in  grm. 

Grm.  per  oz. 

*  This  is  often  called  the  zero  error. 

f  Select  some  body  weighing  100  to  200  grin.     In  a  general  way, 
the  heavier  the  body,  the  more  accurate  the  results. 


84 


MENSURATION. 


EXERCISE  6. 

EXPERIMENT. 

Apparatus.— Part  I.    Meter-stick;  blocks  of  wood;  lead-pencils; 
books;  etc. 

Part  I.     Tumbler;  measuring-cylinder;  water. 
Part  III.    Scales  and  weights;  bodies  weighing  from  10  g.  to  50  g. 

OBJECT. — To  practise  estimating  values  in  the  Metric 
system. 

MANIPULATION. — Length.  Estimate  carefully,  by  the  eye 
alone,  the  dimensions  of  one  of  the  blocks,  the  meter-stick 
being  out  of  sight.  Record  the  estimate.  Carefully  meas- 
ure the  same  distance  and  record.  Try  this  a  number  of 
times,  varying  the  distances  measured  each  time  until  esti- 
mates on  several  different  lengths  in  succession  come  quite 
near  to  measured  values.  Record  as  follows: 


Estimated. 

Found. 

Difference. 

The  figures  in  the  third  column  are  got  by  finding  the 
difference  between  the  measured  and  the  estimated  dis- 
tances. If  the  estimate  is  less  than  the  true  distance,  the 
difference  has  the  minus  sign;  if  greater,  the  plus  sign.  It 
is  best  to  select  lengths  ending  in  sharp  corners,  distances 
between  points  marked  by  a  pencil,  etc. 

Volume.  Put  some  water  into  the  tumbler,  estimate  the 
volume  in  cu.  cm.  Measure  the  volume,  repeat  with  vari- 
ous volumes,  and  record  as  above.  If  possible,  change  the 
vessel  used  to  hold  the  water. 

Weight.  Estimate  the  weight  of  a  few  bodies  in  grams. 
Weigh  the  bodies, 


NOTES  ON  ERRORS.  85 

Measure  as  accurately  as  possible,  but  do  not  try  to  esti- 
mate too  closely.  It  is  enough  to  get  within  0.5  cm.  of 
correctness  in  length,  one  centimeter  in  volume,  and  one 
gram  in  weight. 

NOTES  ON  ERRORS. 

The  results  of  measurements  are  never  absolutely  correct. 
This  is  because  of  imperfections  in  the  apparatus  and  mis- 
takes of  the  experimenter.  In  physical  experiments,  any- 
thing due  to  these  causes,  which  tends  to  make  results 
incorrect,  is  called  an  error.  Errors  of  the  experimenter 
are  called  Personal  Errors.  For  example,  in  Experiment 
1,  any  mistake  in  estimating  the  fraction  of  a  mm.,  in 
not  reading  the  scale  correctly,  or  not  placing  it  properly 
on  the  table,  would  be  a  personal  error.  Personal  errors 
may  be  often  avoided  by  using  care,  and  their  effect  on  the 
result  may  be  still  further  reduced  by  averaging.  In  esti- 
mating the  fraction  of  a  millimeter,  a  person  is  just  as 
liable  to  over-estimate  as  to  under-estimate  ;  if  he  makes  a 
number  of  determinations,  and  averages  his  results,  the 
over-estimates  and  the  under-esti mates  will  tend  to  neutral- 
ize each  other,  and  the  average  will.be  nearer  the  truth. 
For  this  reason,  in  conducting  an  experiment  calling  for 
measurement,  the  more  careful  the  work,  and  the  greater 
the  number  of  determinations,  the  closer  to  the  truth  will 
be  the  average  result.  Errors  due  to  the  apparatus  are 
called  apparatus  errors.  An  error  which  produces  a  con- 
stant effect,  always  tending  to  make  the  result  too  high 
or  too  low,  is  called  a  constant  error.  For  example,  in 
Method  B,  Ex.  3  (Volume  of  an  Irregular  Body),  when 
the  body  was  removed  from  the  water  it  took  some  water 
with  it.  The  volume  obtained  included  this  water,  and 
was  always  higher  than  the  truth.  Sometimes  the  value 
of  a  constant  error  can  be  determined  and  eliminated. 
Suppose  a  spring-balance  with  no  weight  attached  reads 


86  MENSURATION. 

1  Ib.,  then  every  reading  on  the  balance  will  be  1  Ib.  high, 
and  the  true  weights  can  be  obtained  by  subtracting  1  Ib. 
from  each  weight  as  given  by  the  balance. 

QUESTIONS. — 1.  Why  were  a  number  of  determinations 
made  in  Ex.  1,  and  the  results  averaged  ?  2.  What  were 
some  of  the  personal  errors  in  Ex.  1  ?  What  was  an  appa- 
ratus error  in  Ex.  2?  Were  there  any  constant  errors  in 
this  Exercise  ?  Prepare  a  list  of  the  personal  and  appara- 
tus errors  in  each  experiment  in  this  chapter,  with  sug- 
gestions for  their  avoidance. 

EXERCISE  7. 

PHYSICAL  AND    CHEMICAL   CHANGE. 

Preliminary. — Are  physical  and  chemical  changes  accom- 
panied by  change  in  weight?  As  good  examples  of  physi- 
cal change  we  may  take,  first,  the  solidifying  of  a  liquid 
(that  is,  the  changing  of  it  from  a  liquid  to  a  solid  when 
cooled),  and,  second,  the  dissolving  of  a  solid,  in  both  cases 
observing  the  weight  before  and  after  the  change.  In 
selecting  an  example  of  chemical  change,  we  must  take 
two  substances  whose  union  will  give  a  new  substance,  mix 
known  weights  of  each,  and  weigh  the  products.  We  can 
then  compare  the  weight  of  the  new  substance  formed, 
with  the  sum  of  the  weights  of  the  original  substance. 

EXPERIMENT   1. 

Apparatus. — Scales  and  weights;  test-tube  and  fine  wire  to  sus- 
pend it;  shavings  of  wax  or  paraffiue;  means  of  heating;  bits  of 
solid  caustic  potash;  water;  solutions  "No.  1"  and  "No.  2"  ;  two 
small  vessels  in  which  liquids  may  be  weighed. 

OBJECT. — To  see  if  the  weight  of  substances  is  the  same 
before  and  after  a  physical  change. 

MANIPULATION. — (a)  Place  some  scraps  of  wax  or  paraf- 
fine  in  a  test-tube.  Suspend  the  tube  from  one  end  of  a 
balance  and  gently  warm  it  until  the  solid  melts,  Counter* 


NOTES  ON  ERRORS.  87 

poise  and  watch  while  the  contents  of  the  tube  cool  again. 
What  sort  of  a  change  have  you  here  ?  How  do  the  weights 
of  the  solid  and  liquid  compare  ?  (b)  Suspend  a  test-tube 
half  full  of  water  from  one  arm  of  your  balance,  by  means 
of  a  thread,  and  place  a  small  piece  of  caustic  potash  on  a 
scrap  of  paper  in  the  pan.  Counterpoise.  Drop  the  solid 
into  the  water,  leaving  the  paper  on  the  pan.  Watch  for 
any  change  in  weight  while  the  solid  dissolves  in  the  liquid. 
What  sort  of  a  change  is  this  ?  What  is  your  inference  ? 
If  these  experiments  illustrate  a  general  law  as  regards 
change  of  weight  during  a  physical  change,  what  do  you 
infer  the  law  to  be  ? 

EXPERIMENT  2. 

OBJECT. — To  see  if  the  weight  of  substance  is  the  same 
before  and  after  a  chemical  change. 

MANIPULATION". — Put  a  small  glass  vessel  on  the  left- 
hand  scale-pan  and  record  the  weight.  Add  a  10-gram 
weight  to  the  right-hand  scale-pan.  Pour  some  of  solu- 
tion No.  1  slowly  into  the  vessel  until  it  nearly  balances 
(in  all  probability  you  cannot  get  it  to  exactly  balance) ; 
change  the  weight  on  the  scale-pan  until  you  have  the 
exact  weight  of  the  vessel  +  the  liquid.  Record  and  find 
the  weight  of  the  solution  alone.  Weigh  in  the  same  man- 
ner a  part  of  solution  No.  2.  The  quantity  must  be 
exactly  determined,  but  need  not  be  exactly  equal  to  that 
used  of  No.  1.  Pour  the  contents  of  one  vessel  into  the 
other ;  note  what  occurs,  and  weigh  the  whole.  From  this 
weight  subtract  the  weight  of  the  vessel,  and  you  have  the 
weight  of  the  contents.  Compare  this  weight  with  the 
sums  of  the  weights  of  the  two  liquids.  Have  we  changed 
our  forms  of  matter  ?  Is  this  change  chemical  or  physi- 
cal ?  During  a  chemical  change,  what  is  true  as  regards 
the  weight  of  matter?  This  experiment  illustrates  a  gen- 


88  MENSURATION. 

eral  law.     From  your  work,  can  you  state  the  law  ?    Ar- 
range the  results  as  follows  : 

Weight  of  solution  No.  1  -f-  vessel  =  grm. 

"       "  vessel  =  " 

"       "   solution  alone  =  " 

"      "  solution  No.  2  +  vessel  =  " 

"      "  vessel  =  " 


"  "  solution  alone  =  " 

"  "  two  solutions  -f-  vessel  =  (i 

11  "  vessel  = 

"  "  two  solutions  alone  =  " 

"  "  No.  1  =  " 

"  "  No.  2 


"  both  solutions  weighed  separately  = 


DENSITY  AND  SPECIFIC  GEAYITY. 
EXERCISE  1. 

DENSITY  AND  ITS  DETERMINATION. 

Preliminary. — The  same  weight  of  matter  may  take  up 
a  great  deal  of  room  or  only  a  little.  We  express  this 
quality  of  bodies  by  the  words  "heavy"  and  "light." 
When  we  say  that  a  body  is  "  light/'  we  mean  that  the 
space  it  occupies,  its  volume,  is  great  compared  with  its 
weight,  and  by  the  use  of  the  word  "heavy"  we  mean  the 
reverse.  In  using  these  words  we  always  refer  to  some 
other  bodies.  Thus,  when  we  say  that  gas  is  light,  we 
mean  that  the  relation  of  its  volume  to  its  weight  is 
smaller  than  that  of  most  bodies.  Suppose,  now,  we  com- 
pare a  stone  and  a  piece  of  lead.  By  very  rough  tests  we 
can  determine  which  is  the  heavier  ;  but  if  any  exact  com- 
parison is  desired,  the  relation  of  volume  and  weight  must 
be  expressed  as  a  number.  To  get  this  number,  we  must 
measure  the  volume  and  weight  of  each  body,  and  divide 
the  weight  by  the  volume.  The  quotient  shows  how  many 
times  the  volume  number  is  contained  in  the  weight  num- 
ber. A  number  which,  like  this,  expresses  the  number  of 
times  one  quantity  is  contained  in  another  is  called  a  ratio. 
The  ratio  of  the  weight  of  a  body  to  its  volume  is  called 
the  density  of  the  body.  By  comparing  the  density  num- 
ber for  lead  with  the  density  number  for  stone,  we  can 
determine  just  how  many  times  the  lead  is  denser  than  the 
stone.  Density  is  sometimes  represented  by  the  sign  A  ;  * 

*  Called  delta. 


90  DENSITY  AND  SPECIFIC  GRAVITY. 


and  so  we  can  write*  A  =  —  ,  or  density  is  the  weight  of 

the  unit  of  volume.     Would  these  numbers  be  the  same 
for  different  systems  of  measurement  ? 

EXPERIMENT. 

Apparatus.—  Scales  and  weights  ;  8-oz.  balance  or  English 
weights  ;  measuring-cylinder  ;  bodies  whose  densities  are  to  be 
determined  ;  measuring-sticks  (English  and  French). 

OBJECT.  —  To  determine  (1)  the  density  of  the  given 
substances  (a)  in  the  Metric  system,  (b)  in  the  English 
system,  ounces  to  the  cubic  inch  and  pounds  to  the  cubic 
foot  ;  and  (2)  the  order  in  which  the  substances  should  be 
arranged  as  regards  density. 

MANIPULATION.  —  (a)  Determine  the  weight  of  each 
body  in  grams,  weighing  to  0.1  grm.  and  its  volume  in 
cu.  cm.  If  the  body  is  a  geometrical  figure,  measure  the 
dimensions  of  the  figure  and  calculate  the  volume.  If  the 
body  is  irregular,  get  its  volume  by  one  of  the  methods 
given  in  the  exercises  on  mensuration.  Find  the  density 
by  dividing  the  weight  by  the  volume.  Carry  this  number 
out  to  the  second  decimal  place. 

(b)  Determine  the  weight  of  each  body  in  ounces  by  a 
spring-balance,!  expressing  fractions  of  an  ounce  as  deci- 
mals. If  possible  measure  the  volume  in  cu.  in.;  if  it  is 
not  possible,  calculate  the  volume  in  cu.  in.  from  the  vol- 
ume in  cu.  cm.,  as  already  found.  1  cu.  cm.  =  0.061  cu. 
in.;  hence,  Vol.  in  cu.  cm.  X  0.061  —  vol.  in  cu.  in.  Cal- 
culate the  density  in  English  measure,  (1)  ounces  per  cu. 
in.,  (2)  pounds  per  cu.  foot.  Arrange  the  results  in  two 
tables,  heading  the  first  table,  "  Table  I,  French,"  and  the 
second,  "Table  II,  English,  as  follows:" 

*  Such  an  algebraic  arrangement  of  symbols,  as  a  short  way  of 
giving  a  rule,  is  called  a  formula. 
f  An  8-oz.  balance  is  the  best. 


DENSITY  AND  ITS  DETERMINATION. 

TABLE  I,  FRENCH. 


Body. 

Weight. 

Volume. 

Density. 

(2)  Arrange  the  bodies  in  the  order  of  their  densities, 
that  having  the  greatest  density  heading  the  list. 

Weigh  the  liquid  in  a  small  vessel  in  the  usual  way.  In 
case  the  vessel  is  too  large  for  the  scale-pan,  make  a  bale 
of  string  or  wire,  like  the  handle  of  a  pail,  and  suspend 
the  vessel  below  the  scale-pan,  as  in  Fig.  62.  Be  careful 
that  the  string  or  wire  by  which  it  is  suspended  does  not 
break,  and  allow  it  to  drop. 

Unit  of  Density.— We  need  some  standard  with  which 
to  compare  densities.  Some  density  must  be  taken  as  the 
unit,  and  all  densities  expressed  in  terms  of  that  unit. 
The  density  of  water  at  a  specified  temperature  is  used  as 
the  unit  for  solids  and  liquids,  and  that  of  air  under  fixed 
conditions  of  temperture  and  pressure,  for  gases.  In  com- 
paring the  densities  of  solids  or  liquids,  we  take  the  num- 
bers obtained  by  dividing  each  density  by  that  of  water. 

Specific  Gravity. — The  number  which  shows  how  many 
times  the  density  of  water  is  contained  in  the  density  of 
any  solid  or  liquid  is  called  the  Specific  Gravity  of  that 
body.  If  the  destiny  of  iron  were  437.5  Ibs.  per  cu.  ft., 
its  specific  gravity  would  be  found  by  dividing  its  density, 
437.5  Ibs.  by  62.5  Ibs.,  which  is  the  density  of  water  ex- 
pressed in  the  same  system.  We  find  that  the  density  of 
iron  is  seven  times  that  of  water,  hence  the  specific  gravity 
of  iron  is  7.  Calculate  the  specific  gravities  of  the  bodies 
whose  densities  you  determined  in  Exercise  1.  Are  the 
specific-gravity  numbers  the  same  for  all  the  systems  of 
measurement  used  ? 


92  DENSITY  AND  SPECIFIC  GRAVITY. 

EXERCISE  2. 

DETERMINATION  OF  SPECIFIC  GRAVITY. 

Preliminary. — In  order  to  determine  the  specific  gravity 
of  a  body  we  could  get  its  density,  as  in  Ex.  1,  by  dividing 
its  weight  by  its  volume.  The  density  so  obtained  would 
be  divided  by  the  density  of  water  (if  not  known,  this 
would  have  to  be  found)  ;  the  quotient  would  be  the  spe- 
cific gravity  of  the  body.  Or,  again,  to  simplify  the  pro- 
cess, we  could  take  equal  volumes  of  water  and  the  body 
under  examination.  Thus,  if  any  volume  of  a  body  weighs 
50  grm.,  and  an  equal  volume  of  water  weighs  10  grm., 
then  the  density  of  the  body  is  five  times  that  of  the  water, 
and  the  specific  gravity  is  five. 

Suppose  we  take  a  bottle,  weigh  it,  then  fill  it  completely 
full  of  water  and  weigh  it  again.  The  weight  of  the 
bottle  subtracted  from  the  combined  weight  of  the  bottle 
and  water  gives  the  weight  of  the  water.  Suppose,  now, 
we  empty  the  water  completely  out,  and  fill  the  bottle  with 
the  liquid  whose  specific  gravity  we  wish  to  determine. 
Then,  since  we  have  the  same  bottle,  and  have  filled  it 
completely  full,  we  have  the  same  volume  of  liquid  that 
we  took  of  water.  If  we  weigh  the  bottle  and  liquid 
together,  and  subtract  the  weight  of  the  bottle,  we  get  the 
weight  of  the  liquid.  Having  the  weights  of  equal  bulks 
of  water  and  the  liquid,  we  can  get  the  specific  gravity 
of  the  liquid  by  dividing  the  weight  of  the  liquid  by  the 
weight  of  the  water. 

EXPERIMENT. 

Apparatus.— Scales ;  weights ;  specific-gravity  bottle ;  liquid  whose 
specific  gravity  is  to  be  determined;  water. 

OBJECT. — To  determine  the  specific  gravity  of  a  liquid 
by  the  method  of  the  "  Specific-gravity  Bottle." 


DETERMINATION  OF  SPECIFIC  GRAVITY.        93 


MANIPULATION. — Weigh  the  bottle  with  the  stopper  in. 
Be  sure  that  it  is  perfectly  dry.     Fill  it  | — | 

to  the  top  with  the  liquid,  and,  holding  it 
over  some  vessel  to  catch   the  overflow, 
slowly  insert  the  stopper  squarely,  as  in 
Fig.  61.     During  this  operation  the  liquid 
should  run  over  the  rim  of  the  bottle  all 
around.     With  care,  the  bottle  will   be 
completely  filled.     To  test  this,  turn  the 
bottle  upside   down  and   see   if  any  air 
bubbles  appear.     If  they  do,  the  bottle  is 
not  entirely  full,  and  the  operation  of  fill- 
ing must  be  repeated.     Wipe  the  outside 
of  the  bottle  dry  and  weigh  it.     Pour  the  liquid  back  into 
the  "  stock-bottle,"  rinse  the   gravity-bottle,   fill    it  com- 
pletely with  water  with  the  same  precautions  as  before,  and 
weigh  it.     Arrange  results  as  follows : 
Wt.  bottle  +  liquid  = 

"        "    alone          = 


FIG.  61. 


Wt.  bottle  +  water  = 

"    alone  = 

"    water      "  = 
_  Wt.  of  liquid  _ 


"    liquid    " 


QUESTIONS. — 1.  What  is  the  principle  of  this  experi- 
ment? 2.  Why  must  you  be  sure  that  the  bottle  is  com- 
pletely full  each  time  ?  3.  What  do  you  consider  the  most 
important  error  that  is  likely  to  be  made?  4.  Why  must 
the  same  bottle  be  used  each  time  ?  5.  Why  should  the 
bottle  be  rinsed  out  before  filling  it  with  water  ? 

EXERCISE  3. 

THE  WEIGHT  LOST  BY  A  BODY  WHEN  IMMERSED  IN  A  LIQUID. 

Preliminary. — We  know  that  a  body  does  not  weigh  as 
much  under  water  as  it  does  above,  and  that  when  it  is 


94  DENSITY  AND  SPECIFIC  GRAVITY. 

completely  immersed  it  displaces  a  volume  of  water  equal 
to  its  own  volume.*  The  object  of  the  following  exercise  is 
to  see  if  there  is  any  connection  between -this  loss  of  weight 
and  the  weight  of  the  water  displaced.  On  what  principle 
must  we  work  in  order  to  be  able  to  make  this  compari- 
son? 

In  order  to  get  the  loss  of  weight,  we  can  weigh  the  body 
in  air  and  then  in  water.  The  difference  is  the  body's 
loss  of  weight.  To  weigh  the  water  displaced,  we  can  fill 
the  specific-gravity  bottle  completely  full  of  water,  and 
weigh  it  and  the  body  together.  Then  if  we  put  the  body 
into  the  bottle  it  will  crowd  out  a  volume  of  water  equal 
to  its  own  volume.  If,  after  inserting  the  stopper,  we 
weigh  the  bottle  with  the  remaining  water  and  the  body, 
the  weight  will  be  less  than  before  by  the  weight  of  the 
water  crowded  out.  This  difference  is  the  weight  of  the 
displaced  water.  Having  found  the  body's  loss  of  weight 
and  the  weight  of  the  displaced  water,  we  can  see  if  there 
is  any  connection  between  the  two  facts. 

EXPERIMENT. 

Apparatus.— Specific-gravity  bottle;  water;  scales  and  weights; 
solid  body;  fine  wire  for  suspension;  tumbler. 

OBJECT. — To  compare  the  weight  lost  by  a  body  when 
immersed  in  a  liquid,  with  the  weight  of  a  volume  of  the 
liquid  equal  to  the  volume  of  the  body. 

MANIPULATION". — Fill  the  specific-gravity  bottle  full  of 
water  and  place  it  in  the  scale-pan.  Place  the  body  in  the 
same  pan  and  weigh  both.  Take  the  stopper  out  of  the 
bottle,  put  in  the  body,  replace  the  stopper,  wipe  the  bottle 
dry  and  weigh  again.  The  difference  in  the  weights  is  the 
weight  of  the  water  crowded  out  of  the  bottle  when  the 
body  was  put  in,  and  hence  the  weight  of  a  volume  of 
water  equal  to  the  volume  of  the  body. 

*  Provided,  of  course,  the  liquid  does  affect  on  tbe  solid. 


BODT  IMMERSED  IN  A  LIQUID— WEIGHT  LOST-  95 

To  get  the  body's  loss  of  weight  in  a  liquid,  suspend  it 
by  a  thread,  or,  better,  a  fine  wire,  which,  as  shown  in  Fig. 
62,  passes  through  holes  in  the  scale-pan  and  box,  and  is 
attached  to  the  scale  arm-hook.  Weigh.  Put  a  tumbler 
of  water  under  the  box  and  adjust  it  so  that  the  body  is 


FIG.  62. 

completely  immersed  in  the  liquid  and  touches  neither  the 
sides  nor  the  bottom.  Weigh  the  body,  being  careful  to 
keep  it  entirely  under  water.  If  time  allows,  repeat  with 
some  other  liquid.  Record  results  as  follows  : 

Bottle  +  water  -f-  body  outside  = 

"      +      "     +    "     inside     = 

Weight  of  water  displaced          = 

Weight  of  body  in  air  = 

"      "     "     "  water  = 

Loss  of  weight  = 


96          DENSITY  AND  SPECIFIC  GRAVITY. 

EXERCISE  4. 

THE  DETERMINATION  OF  SPECIFIC  GRAVITY  BY  IMMERSION. 

Preliminary. — It  is  evident  that  the  method  of  the  spe- 
cific-gravity bottle  cannot  be  used  for  solids,  and  so  the 
principle  of  the  preceding  exercise  is  employed  in  deter- 
mining the  weight  of  the  water  equal  in  bulk  to  the  solid 
whose  specific  gravity  is  required.  By  weighing  the  solid 
in  air  and  then  in  water  we  can  get  its  loss  of  weight,  which 
last,  we  have  found,  is  also  the  weight  of  an  equal  volume 
of  water.  We  then  have  the  weight  of  the  body  and  the 
weight  of  an  equal  volume  of  water,  and  can  calculate  the 
specific  gravity. 

The  same  principle  can  be  used  in  getting  the  specific 
gravity  of  liquids.  By  ascertaining  the  loss  of  weight  of 
a  solid  in  water,  we  get  the  weight  of  a  volume  of  water 
equal  to  the  volume  of  the  solid.  By  finding  the  loss  of 
weight  of  the  same  solid  in  the  liquid  whose  specific  gravity 
is  to  be  determined,  we  get  the  weight  of  a  volume  of  the 
liquid  equal  to  the  volume  of  the  solid.  The  body  being 
the  same,  we  have  the  weights  of  equal  volumes  of  the 
liquids,  and  can  compute  the  required  specific  gravity. 

EXPERIMENT   1. 

Apparatus.— Scales  and  weights;  body  and  wire  for  suspension; 
tumbler;  liquid  whose  specific  gravity  is  to  be  determined;  water. 

OBJECT. — To  determine  the  specific  gravity  of  a  solid 
not  affected  by  water,  and  of  a  liquid,  by  the  method  of 
"  Double  Weighing." 

MANIPULATION.— Part  I.  Suspend  the  solid  by  a  thread 
or  fine  wire,  as  in  the  preceding  exercise  (Fig.  62).  Care 
must  be  taken  not  to  let  the  solid  touch  the  glass  at  any 
point.*  Weigh  the  solid  as  closely  as  can  be  done  on  the 

*  With  an  irregular  body,  a  glass  stopper  for  instance,  some  judg- 
ment must  be  exercised  regarding  the  manner  in  whicb  the  bodj-  is 
suspended. 


SPECIFIC  GRAVITY  DETERMINED  BY  IMMERSION.  97 

scales.  Record  the  weight.  Fill  the  tumbler  with  water 
and  weigh  again,  taking  care  that  the  body  is  entirely  im- 
mersed and  touches  neither  the  sides  nor  the  bottom  of 
the  glass,  and  that  the  suspending  thread  does  not  touch 
the  sides  of  the  hole  in  the  box.  Record  as  follows : 

Wt.  in  air       = 
"     "  water  = 


Loss  of    "     "        "    = 

Wt.  in  air  rn  ,  -. 

op.  err.  =  r —  ; — : ; —   =    Carry  out  to  3d  dec.  pi. 

Loss  of  wt.  in  water 

Part  II.  After  weighing  the  body  first  in  air  and  then 
in  water,  and  recording  the  weights,  empty  the  water  out 
from  the  tumbler,  fill  the  tumbler  with  the  given  liquid, 
and  weigh  the  body  again,  using  in  all  cases  the  same  pre- 
cautions as  in  Part  I.  Record  results  as  follows  : 

Wt.  in  air       =  Wt.  in  air        = 

"     "  water  =  "    "  liquid  = 


Loss  of   "     "       "     =  Loss  of    "     "       " 

Loss  wt.  in  liquid 

Sp.  grav.  =  f T-. -  = 

Loss  wt.  in  water 

How  does  this  experiment  compare  in  principle  with  the 
method  of  the  specific-gravity  bottle  ? 

If  Part  II  is  pel-formed  immediately  after  Part  I.,  the 
solid's  loss  of  weight  in  water  is  already  known,  and  we 
have  only  to  weigh  the  solid  in  the  liquid  whose  specific 
gravity  is  required.  The  record  would  then  take  the  fol- 
lowing form : 

[From  Part  I.]  Wt.  in  air       = 

"      "  liquid  = 

Loss  of  "     "        "      = 
[From  Part  L]       "     «    "    «  water    = 


98          DENSITY  AND  SPECIFIC  GRAVITY. 

0  Loss  of  wt.  in  liquid 

Sp.  grav.  =  T 5 —  —. —       -  = 

Loss  of  wt.  in  water 

EXPERIMENT  2. 

Apparatus. — Scales  and  weights;  water;   tumbler;  body  lighter 
than  water;  sinker;  thread  or  fine  wire. 

OBJECT. — To  determine  the  specific  gravity  of  a  body 
that  will  float  in  water. 

MANIPULATION". — Weigh  the  body  in  air.     Attach  the 
sinker  close  to  the  body  with  thread  or  wire;  suspend  the 
two,  as  in  the  previous  experiment,  and  with  the  same 
precautions  determine  the  weight  of  the  two  in  air.     De- 
termine the  weight  of  the  two  when  immersed  in  water,  in 
the  same  way  as  in  the  previous  experiment.     Remove  the 
body  and  determine  the  weight  of  the  sinker  alone  when 
immersed  in  water.*     Arrange  results  as  follows: 
Sinker  -j-  body  in  air  — 
'•'      alone  in  air      = 
Body  in  air  = 

Sinker  in  water 

CALCULATION. — Arrange  calculations  as  follows: 
Sinker  -J-  body  in  air       =  Sinker  in  air       = 

"  "      "  water  =  "       "  water  = 


Loss  of  wt.  of  both  in  water  =        Loss  of  wt.  of  sinker  = 
Loss  of  wt.  of  body  -f  sinker  = 
"      u    "     "  sinker  alone      = 


"     "    "    "  body        " 

o         f      Wt.  of  body  in  air 

~~  Loss  of  wt.  of  body  in  water  ~~ 

*  The  number  of  operations  involved  in  this  experiment  may  be 
reduced  by  taking  the  data  obtained  in  Experiment  1,  which  may 
be  done  by  using  for  a  sinker  the  body  whose  specific  gravity  was 
there  determined.  It  is  then  only  necessary  to  ascertain  the  weight 
of  the  sinker  plus  the  body  in  air  and  the  loss  of  weight  of  both  in 
water. 


LIQUID  PRESSURE  DUE  TO    WEIGHT. 


99 


Questions. — 1.  In  these  experiments,  is  the  weight  of  the 
equal  volume  of  water  actually  measured  at  all  ?  2.  Why 
are  you  justified  in  taking  the  loss  of  weight  as  the  weight 
of  a  bulk  of  water  whose  volume  equals  that  of  the  body? 
3.  State  the  principles  of  this  experiment.  4.  How  does 
it  differ  from  that  used  in  getting  the  specific  gravity  of  a 
liquid  ? 

EXERCISE  5. 

LIQUID  PRESSURE  DUE  TO   WEIGHT. 

Preliminary. — For  investigating  the  conditions  affecting 
liquid  pressure,  we  use  the  apparatus  shown  in  Fig.  63.  A 
pressure-gauge  is  made  of  a  glass  funnel,  «,  whose  end  is 


FIG.  63. 


covered  with  thin  rubber,  k.     From  the  other  end,  a  rubber 
tube,  I,  connects  the  funnel  with  the  glass  tube,  cd,  which 


100  DENSITY  AND  SPECIFIC  GRAVITY. 

is  attached  to  the  scale,  w,  and  contains  a  drop  of  water, 
d,  to  act  as  an  index.  Changes  of  pressure  will  cause  the 
rubber,  k,  to  bulge  more  or  less,  and  this  will  cause  a 
motion  of  the  index  which  can  be  read  upon  the  scale. 
This  gauge  is  hung  from  the  block,  e,  by  a  wire  on  which 
it  turns,  so  that  it  may  be  made  to  face  in  any  direction 
and  the  centre  of  k  remain  at  the  same  depth.  To  this 
block  is  attached  a  meter-stick,  /,  which  indicates  the 
depth.  The  apparatus  is  held  by  a  clamp,  g,  and  is  placed 
in  a  pail  of  water,  h.  The  scale  m  lies  flat  upon  the  table. 

EXPERIMENT. 

Apparatus.— As  shown  in  Fig.  63.  Water  and  pail  (or  equivalent); 
measuring-cylinder  (or  something  that  can  be  used  to  produce 
changes  in  depth  directly  over  the  gauge-face.) 

OBJECT. — To  investigate  the  conditions  affecting  the 
pressure  of  a  liquid  upon  a  surface  immersed  in  it. 

MANIPULATION. — Before  commencing  the  experiment 
it  is  necessary  to  know  how  the  movements  of  the  index 
correspond  with  changes  in  pressure.     The  gauge  being  in 
the  water,  press  on  its  face  gently  with  the  finger  and  note 
the  direction  of  the  movement  of  the  index.     Remove  the 
pressure  and  note  again.     Record  the  direction  of  move- 
ment for  increased  and  decreased  pressure,  as  follows  : 
Increased  pressure-index  moves 
Decreased       " 

Part  I.  Effect  of  depth.  The  gauge-face  being  1  or  2 
cm.  below  the  level  of  the  liquid,  note  the  position  of  one 
end  of  the  index,  and  the  depth  of  the  gauge.  Increase, 
the  depth  4  or  5  cm.  (most  easily  done  by  setting  the 
clamp  lower  down  on  the  rod),  read  the  depth  and  the 
position  of  the  index.  Be  careful  to  always  read  from 
the  same  end  of  the  index,  to  clamp  the  apparatus  firmly 
at  each  depth,  and  to  wait  for  the  liquid  to  come  to  rest 
before  reading.  In  this  way  take  readings  at  various 
depths,  working  first  down  to  as  near  the  bottom  of  the 


LIQUID  PRESSURE  DUE  TO   WEIGHT. 


101 


vessel  as  is  possible,  and  then  up  again  to  near  the  surface. 
Tabulate  results  as  follows : 


Depth. 

Index-reading. 

From  the  study  of  these  figuures,  place  in  the  note-book 
an  inference  regarding  the  effect  of  depth  on  pressure. 

Part  II.  Effect  of  direction.  Adjust  the  apparatus  so 
that  the  gauge-face  is  6  or  7  cm.  below  the  surface.  Put- 
ting the  hand  into  the  water,  take  the  rubber  tube  gently 
between  the  thumb  and  finger  at  a  point  just  below  where 
it  joins  the  glass,  and  slowly  turn  the  gauge-face  in  various 
directions,  reading  the  index  for  each  direction.  Take 
care  that  there  is  plenty  of  slack  rubber  tube,  and  that  it 
does  not  "  kink"  anywhere.  Make  three  or  four  trials  at 
this  depth,  and  then  repeat  at  some  other.  Kecord  results 
as  follows: 


Depth. 

Direction  of  gauge-face. 

Index-reading. 

"What  inference  ? 

Part  III.  Effect  of  distance  from  sides  of  vessel  at  same 
depth.  Gently  set  the  gauge  at  various  points  at  the  same 
level  by  moving  either  the  arm  of  the  clamp  horizontally 
or  the  pail  under  the  apparatus.  In  each  case  wait  for  the 
liquid  to  come  to  rest,  read,  and  record  as  follows  : 


Depth. 

Position  relative  to  vessel  sides. 

Index-reading. 

What  inference  ? 


102 


DENSITY  AND  SPECIFIC  GRAVITY. 


Part  IV.  Effect  of  depth  of  liquid  directly  over  the 
immersed  body.  Tip  the  apparatus  sideways  as  shown  in 
Fig.  64,  and  clamp  it  there.  Bring  the  bottom  of  a  glass 


FIG.  64. 

cylinder  down  over  the  gauge-face,  as  in  the  figure.  This 
reduces  very  much  the  depth  and  amount  of  the  liquid 
directly  over  the  gauge-face,  but  does  not  change  the  gen- 
eral level  of  the  liquid  to  a  noticeable  degree.*  Immerse 
the  bottom  of  the  cylinder  to  various  distances  above  the 
gauge-face.  Read  the  index  each  time.  At  each  point 
hold  the  cylinder  steady  and  wait  until  the  water  in  the 
pail  has  come  to  rest  before  reading  the  index.  To  in- 
crease the  depth  of  liquid  directly  over  the  gauge-face, 
submerge  the  cylinder  completely  and  invert  it.  Holding 
the  inverted  cylinder  by  the  bottom,  raise  it  until  the  lower 
end  is  only  one  or  two  cm.  below  the  level  of  the  liquid. 
So  long  as  no  air  enters,  the  water  will  remain  in  the  cylin- 
der, and  by  bringing  it  over  the  gauge-face,  as  in  Part  IV, 
the  depth  of  water  there  may  be  made  considerably  greater 

*  Of  course,  the  larger  the  pail,  the  less  this  error  amounts  to. 


SPECIFIC  ORA  VITY  OF  LIQ  UIDS  BY  BALANCING.    103 

than  elsewhere  in  the  pail.  The  admission  of  air  into  the 
cylinder,  by  raising  one  edge  for  an  instant  above  the  level 
of  the  liquid,  will  enable  you  to  change  the  depth  of  water 
in  it.  In  this  way  try  various  depths.  Eecord  results  as 
follows : 


Depth  of  Gauge-face  below 
General  Surface. 

Depth  Liquid  directly 
above  Gauge-face. 

Index- 
reading. 

What  inference  ? 

Write  out  a  summary  of  what  you  have  learned  about  all 
the  conditions  affecting  the  pressure  that  the  weight  of  a 
liquid  causes  it  to  exert  on  an  immersed  surface. 

EXERCISE  6. 

SPECIFIC  GRAVITY  OF  LIQUIDS  BY  THE  METHOD  OF  BALANCING. 

Preliminary. — In  the  following  exercise  we  wish  to  de- 
termine the  specific  gravity  of  a  liquid  by  the  method  of 
balancing.  This  method  is  based 
on  the  laws  of  liquid  pressure. 
Suppose  we  have  two  tubes,  con- 
nected as  at  a  in  Fig.  65.  Pour 
some,  liquid  into  one  tube,  and  a 
liquid  that  will  not  mix  with  it 
into  the  other.  Then,  when  the 
liquids  have  come  to  rest,  we  shall 
have  two  columns  balancing  each 
other.  Where  the  two  liquids  join, 
a,  there  are  two  pressures — a  down- 
ward pressure  due  to  the  weight  of 
the  liquid  above,  and  an  upward 
pressure  due  to  the  liquid  in  the  other  tube,  When  the 


Fia.  65. 


104  DENSITY  AND  SPECIFIC  GRAVITY. 

liquids  have  come  to  rest,  we  know  that  these  pressures  are 
equal.  Call  the  upward  pressure  P,  and  the  downward 
pressure  P';  then  P  =  P'.  But  we  know  that 

P  =.  a  X  D  X  A, 
and 

P'  =  a'  X  D'  X  4', 

calling  a',  D',  and  A'  the  values  for  the  second  liquid.     So 
a  X  D  X  A  =  a'  X  D'  X  A'. 

But  as  the  pressures  come  together  in  the  same  tube  at  the 
same  point,  a  =  a',  so  when  two  liquids  come  to  rest  in 
communicating  vessels, 

D  X4  =  D'  X4' 


or,  the  depth  times  the  density  of  one  equals  the  depth 
times  the  density  of  the  other.  Hence,  to  determine  the 
required  density,  we  have  only  to  put  into  one  tube  a  liquid 
of  known  density,  into  the  other  the  liquid  under  examina- 
tion, measure  the  depths  of  the  two  liquids,  and  divide  the 
product  of  the  density  and  depth  of  the  former  by  the 

depth  of  the  latter,  or    A'  =  -  TV""" 

EXPERIMENT. 

Apparatus.—  As  shown  in  Fig.  66.  Funnel;  water  and  oil—  with 
vessels  to  contain  them;  meter-stick;  solution  of  copper  sulphate 
or  equivalent. 

OBJECT.  —  To  determine  the  specific  gravity  of  a  liquid 
by  the  method  of  balancing.* 

*  Observe  that  this  special  method  can  only  be  used  for  liquids 
that  do  not  mix, 


SPECIFIC  GRA  VITT  OF  LIQUIDS  BY  BALANCING.    105 


-F  —-B 


I c 


MANIPULATION. — By  the  aid  of  the  funnel,  pour  water 
into  the  tube  until  it  stands  about  half-way  up  in  both 
branches.  Make  sure  that 
no  air  remains  in  the  rub- 
ber tube  by  drawing  the 
tube  through  the  fingers 
pressed  together.  Slowly 
pour  the  oil  into  the  larger 
tube,  at  first  letting  it  run 
down  the  sides  so  as  to  ac- 
cumulate quietly  on  top  of 
the  water,  and  continu- 
ing until  the  column  is 
50  cm.  or  so  long.  Care 
must  be  taken  that  the 
junction  of  the  liquids  does 
not  get  below  the  glass  into 
the  rubber  tube.  In  case 
this  happens,  it  can  some- 
times be  remedied  by  pour- 
ing more  water  into  the 
water  tube.  Avoid  getting 
the  oil  into  the  water  tube. 
When  the  liquids  have  come  to  rest,  starting  from  some 
horizontal  line  below  the  tubes,  as  D,  Fig.  60  (the  floor, 
the  base-board,  or  the  table  will  do),  measure  the  distance: 

(a)  from  the  reference-line  to  the  top  of  the  water  col- 
umn, or  DA; 

(b)  from  the  reference-line  to  the  top  of  the  other  col- 
umn, DB\ 

(c)  from  the  reference-line  to  the  junction  of  the  liquids, 
marked  DC. 

CALCULATION.     BD  —  CD  =  Height  of  the  column  of 
the  liquid  whose  specific  gravity  is  to  be  determined,  ancj 


i 

a  s 

r 

3 

a  B 

%m^ 

i 

I 

J3 

FIG.  66. 


106 


DENSITY  AND  SPECIFIC  GRAVITY. 


AD  —  CD  =  Height  of  the  water  column  producing  the 
same  pressure  on  the  same  area.     Therefore 

A-  C 


Sp.  grav.  = 


B-  C 


Make  three  or  four  determinations  with  various  heights, 
changing  the  heights  by  pouring  in  either  water  or  oil. 
Tabulate  results  as  follows: 


TABLE  I. 


BD 

AD 

CD 

BD  -  CD 

AD  -CD 

Sp.  Grav. 

If  time  allows,  repeat,  using  solution  of  copper  sulphate 
as  the  liquid  whose  specific  gravity  is  to  be  determined, 
and  the  oil  as  the  liquid  of  known  density,  taking  for  its 
specific  gravity  the. average  of  three  trials  with  water. 


EXERCISE  7. 

EXPERIMENT    1. 

Apparat us.— Loaded  test-tube  with  cork  and  weights;  measuring- 
cylinder;  water;  other  liquids  of  known  density. 

OBJECT. — To  compare  the  weight  of  a  body  that  will 
float  with  the  weight  of  the  liquid  displaced  by  the  body 
when  floating. 

MANIPULATION. — Weigh  the  test-tube;  pour  about  30 
cu.  cm.  of  some  liquid  into  the  measuring-cylinder,  care- 
fully rend  the  volume,  and  holding  the  test-tube  by  the 
cork,  let  it  slip  gently  into  the  liquid  until  it  floats.  Be 
careful  that  the  measuring-cylinder  is  dry  above  the  level 
of  the  liquid  after  the  test-tube  is  inserted.  In  order  that 
the  body  may  float  freely,  tap  the  measuring-cylinder  sev- 
eral times  with  a  lead-pencil.  Again  read  the  volume  of 


ATMOSPHERIC  PRESSURE  AND  THE  BA&O METER.   107 

the  liquid.  The  difference  in  the  readings  gives  the  vol- 
ume of  liquid  displaced  by  the  body,  and  this  volume 
multiplied  by  its  density  gives  the  weight.  Repeat  the 
determination  with  two  other  liquids.  Record  results  as 
follows: 


Vol.  before. 

Vol.  after. 

Vol.  displaced. 

Weight 
displaced. 

Liq. 
used. 

Wt.  of 
Body. 

EXPERIMENT   2. 

OBJECT. — To  determine  the  specific  gravity  of  a  liquid 
by  the  use  of  a  floating  body. 

MANIPULATION. — With  the  apparatus  above,  determine 
the  specific  gravity  of  another  liquid,  writing  out  in  the 
note-book  a  complete  statement  of  the  special  method,  etc. 

QUESTIONS. — 1.  State  the  principle  of  these  experiments. 
2.  How  does  it  differ  from  that  on  which  the  preceding 
exercises  were  based  ?  3.  How  does  the  loss  of  weight  of 
the  body  compare  with  its  weight  in  air?  4.  Do  you  think 
this  fact  had  any  connection  with  the  floating  of  the  body  ? 


EXERCISE   8. 

ATMOSPHERIC  PRESSURE  AND  THE  BAROMETER. 

EXPERIMENT. 

Apparatus.— Barometer  tube;  clamp;  handkerchief  or  cloth;  mer- 
cury (about  1  k.)  funnel ;  feather  on  wire  for  removing  air-bubbles  ; 
dish  to  hold  mercury;  meter-stick;  scales  and  weights;  beaker  glass 
for  weighing  mercury. 

OBJECT. — To  measure  the  pressure  of  the  atmosphere. 

MANIPULATION. — Clamp  the  barometer-tube  in  an  up- 
right position,  closed  end  down,  placing  under  it  some  soft 
substance,  as  a  handkerchief  or  towel.  By  the  aid  of  the 
funnel  fill  the  tube  about  half  full  of  mercury,  then  gently 


10&        DENSITY  AND  SPECIFIC 

insert  the  feather,  and,  by  turning  the  wire,  remove  the 
bubbles  of  air  which  adhere  to  the  side.  Add  10  or  15  cm. 
more  of  mercury  and  repeat  the  removal  of  the  air-bubbles. 
Proceed  in  this  way  until  the  tube  is  filled  with  mercury 
and  contains  no  air.  Have  ready  the  dish  containing  the 
mercury  filled  to  a  depth  of  3  or  4  cm.;  grasp  the  tube 
near  the  top  with  the  right  hand,  placing  the  thumb  firmly 
over  the  opening.  With  the  left  hand  unclamp  the  tube, 
grasp  it  near  the  bottom,  and  (keeping  the  thumb  firmly 
on  the  open  end)  inverting  the  tube,  place  the  end  in  the 
vessel  below  the  level  of  the  mercury.  Kemove  the  thumb 
and  again  clamp  the  tube  vertically,  being  sure  that  the 
clamp  takes  the  weight  of  the  tube,  which  must  not  rest 
on  the  bottom  of  the  vessel.  Observe  and  record  what 
happens. 

When  the  mercury  column  has  come  to  rest,  carefully 
measure  its  height  above  the  level  of  the  mercury  in  the 
vessel.  Placing  the  thumb  loosely  over  the  lower  end  of 
the  tube  and  holding  the  tube  as  before,  raise  it  gently 
until  its  lower  edge  is  just  below  the  level  of  the  mercury, 
then  press  the  thumb  firmly  on  the  bottom,  lift  the  tube 
out,  incline  it  in  a  nearly  horizontal  position,  and  allow  the 
mercury  to  run  very  gently  into  the  thin  glass  vessel  by 
admitting  air,  a  few  bubbles  at  a  time,  into  the  bottom  of 
the  tube.  Be  sure  that  none  of  the  mercury  is  spilled. 
Weigh  the  vessel  with  the  mercury,  and  also  weigh  the 
empty  vessel  and  compute  the  weight  of  the  mercury.  This 
gives  the  pressure  of  the  atmosphere  on  each  area  equal  to 
that  of  the  cross-section  of  the  tube. 

CALCULATION. — To  find  the  cross-section  of  the  tube, 
divide  the  weight  of  the  mercury  by  13.6  to  get  the  vol- 
ume, and  this  quotient  in  turn  by  the  height,  as  in  the  ex- 
periment on  the  Cross-section  of  a  Tube.  To  find  the 
pressure  per  sq.  cm.,  make  the  proportion  A  :  1  sq.  cm.  :: 


SPECIFIC  GftAVtTT  Off  TWO  LIQUIDS.          109 

W  :  W.    Where  A  is  the  area  of  the  tube,  W  is  the  weight 
of  the  mercury,  and  W '  is  the  weight  per  sq.  cm. 

EXERCISE  9. 

SPECIFIC   GRAVITY  OF    TWO   LIQUIDS   BY  BALANCING   AGAINST 
THE    ATMOSPHERIC    PRESSURE. 

Preliminary. — If  we  dip  the  lower  end  of  a  tube  into  a 
liquid  and  remove  a  portion  of  the  air  from  the  tube,  the 
tension  of  the  air  remaining  becomes  less  than  that  of  the 
air  outside,  and  a  column  of  the  liquid  is  forced  up  the 
tube,  until  its  weight,  plus  the  tension  of  the  air  above  it, 
produces  a  pressure  equal  to  the  tension  of  the  air  outside. 
If  we  place  the  tube  in  another  liquid  and  withdraw  the 
same  amount  of  air,  then  the  second  liquid-column  formed 
has  to  furnish  the  same  pressure  as  the  first.  The  two 
columns,  instead  of  being  balanced  against  each  other,  as 
in  Exercise  6,  are  balanced  against  the  same  pressure,  that 
of  the  atmosphere,  and  must  be  of  equal  weight.  So,  as 
before, 

A  X  D  =  A1  x  />'. 

In  the  following  exercise  we  wish  to  determine  the  spe- 
cific gravity  of  a  liquid  by  this  method.  In  order  to  have 
the  same  reduction  of  tension  in  each  tube,  both  are  con- 
nected with  the  same  vessel,  as  in  Fig.  67,  and  the  air  drawn 
out  of  that.  If  one  liquid  has  a  known  density,  we  can 
determine  the  specific  gravity  of  the  other,  by  the  same  cal- 
culation as  in  Exercise  6. 

EXPERIMENT. 

Apparatus. — Form  shown  in  Fig.  67.  Vaseline;  meter-stick;  water; 
solution  of  copper  sulphate  and  some  other  solution. 

OBJECT. — To  determine  the  specific  gravity  of  a  liquid 
that  will  mix  with  water,  by  the  method  of  balancing. 


no 


AND  BPfiOifflO  GRAVITY. 


MANIPULATION*. — Arrange  apparatus  as  in  Fig.  67.  Place 
water  in  one  tumbler  and  in  the  other  the  copper  sulphate- 

By  applying  the  lips  to  the 
glass  mouthpiece  a,  suck 
some  air  out  of  the  bottle 
B,  thus  causing  a  column 
of  liquid  to  rise  in  each 
tube.  Without  removing 
the  mouthpiece  from  the 
lips,  compress  the  tube 
tightly  with  the  left  hand, 
and  while  holding  it  in  this 
manner,  replace  the  mouth- 
piece by  the  solid  plug 
(which  may  be  covered  with 
vaseline).  On  releasing 
the  tube,  the  columns  of 
the  liquids  will  stand  at  a 
certain  height  in  ^ach.  By 
bringing  a  scale  alongside 
the  tube,  the  height  of 
each  column  from  the  level 
of  the  liquid  may  be  ob- 
tained. The  specific  gravity 
FIG.  67.  is  equal  to  the  height  of 

the  water  column  divided 

by  the  height  of  the  other  column.     Repeat  several  times 
with  different  heights.     Tabulate  result : 


Height  of  Water. 

Height  of  other  Liquid. 

Specific  Gravity. 

Keplace  the  water  by  some  other  liquid,  and,  taking  the 


SPECIFIC  G&AVITY  OP  TWO  LfytflDS.         HI 


copper  sulphate  as  the  liquid  of  known  density,  determine 
the  specific  gravity  of  the  other  liquid. 

QUESTIONS.  —  How  does  this  method  differ  in  principle 
from  Exercise  6  ?  With  sufficiently  long  tubes,  could  de- 
terminations of  specific  gravity  be  made  in  this  way  by 
entirely  removing  the  air?  Suggest  a  method  of  determin- 
ing specific  gravity  based  upon  Exercise  8. 


HEAT. 


The  Bunsen  Burner. — The  instrument  commonly  used 
for  heating  bodies  is  a  burner,  called  the  Bunsen  Burner. 
This  instrument  (Fig.  68)  is  con- 
nected with  the  gas-pipe  by  a  rub- 
ber tube,  and  consists  of  a  pipe,  a, 
provided  with  holes  near  the  bot- 
tom, which  can  be  closed,  if  desired, 
by  turning  the  sleeve,  S.  The  gas 
enters  the  bottom  of  the  tube  through 
a  small  opening,  and,  when  lighted 
at  the  top  of  the  tube,  burns  with  a 
very  hot  blue  flame,  free  from  smoke. 
On  shutting  the  air-holes,  the  flame 
becomes  yellow  and  smoky.  Never 
FIG.  es.  use  the  yellow  flame  except  when 

specially  instructed  to  do  it.  It  will  cover  with  a  coating 
of  lamp-black  whatever  is  put  in  it.  When  turned  down 
low,  the  flame  sometimes  runs  down  to  the  bottom  of  the 
tube,  and  burns  at  the  point  where  the  gas  enters.*  This 
is  called  "  backing-down,"  and  is  often  indicated  by  the 
flame  taking  a  green  color.  Backing-down  should  be 
stopped  at  once,  as  it  will  make  the  lamp  very  hot,  some- 
times even  hot  enough  to  melt  the  rubber  tube.  A  smart 
blow  of  the  fist  on  the  rubber  tube  as  it  lies  on  the  table 
will  often  cause  the  flame  to  jump  to  the  top  of  the  tube. 
If  this  fails,  the  gas  must  be  turned  off  and  relighted. 

*  Partially  closing  the  sleeve  when  the  gas  is  turned  low  tends  to 
prevent  this. 

113 


ffOW  SEAT  TRAVELS. 


113 


Precautions  in  Heating. — If  a  flask  is  nearly  full  of 
water,  it  is  fairly  safe  to  heat  it  directly,  but  care  must  be 
used  that  the  flame  strikes  the  glass  nowhere  above  the 
level  of  the  water.  Test  tubes  are  usually  heated  directly 
in  the  flame,  with  the  same  precautions.  They  may  be 
held  by  a  strip  of  paper,  doubled  three  or  four  times,  and 
passed  around  the  tube  near  the  top.*  The  bottom  of 
any  vessel  to  be  heated  should  usually  be  held  about  three 
inches  above  the  top  of  the  burner.  The  safest  way  of 
heating  a  glass  flask  is  by  means  of  a  shallow  saucer  of 
sheet-iron,  filled  with  sand,  in  which  the  bottom  of  the 
flask  rests.  Such  an  arrangement  is  called  a  sand-bath, 
and,  when  the  burner  is  placed  under  it,  should  be  sup- 
ported three  or  four  inches  above  the  top  of  the  tube.  In- 
stead of  a  sand-bath,  a  piece  of  wire-gauze  is  often  used. 
This  is  placed  upon  the  ring  of  the  ring-stand,  and  the 
bottom  of  the  flask  allowed  to  rest  upon  it.  The  flask  may 
break,  and  should  your  hand  happen  to  be  beneath  it,  a 
severe  scalding  may  result.  Be  careful. 

EXERCISE  1. 

HOW  HEAT  TRAVELS. 

Preliminary. — In  the  following  exercise  we  wish  to  ob- 
serve what  happens  when  one  portion  of  a  body  is  raised  to 


B.B. 


FIG.  69. 


a  higher  temperature  than  the  other  portions.     We  may 
use  the  apparatus  shown  in  Fig.  69,  which  consists  of  a 

*  Essentially  as  iu  Fig.  48. 


114 

rod  held  by  the  support  S,  so  that  one  end  may  be  heated 
by  the  burner  BB.  Make  some  pellets  of  wax  a  little 
larger  than  the  head  of  a  pin,  and  place  them  at  regular 
intervals  along  the  upper  side  of  the  rod,  as  aa.  Any  con- 
siderable rise  in  temperature  at  any  point  on  the  rod  will 
be  indicated  by  the  melting  of  the  pellet  there.  We  must 
try  several  rods  of  different  materials,  and  vary  the  condi- 
tions by  bringing  two  different  substances  in  contact,  in- 
stead of  using  different  parts  of  the  same  substance.  Fi- 
nally, we  must  try  a  liquid.  The  case  of  a  liquid  is  a  little 
different,  because  its  particles  are  free  to  move  among 
themselves,  and  we  shall  require  some  means  of  observing 
such  motion  if  it  occurs. 

EXPERIMENT   1. 

Apparatus.— Exp.  1-3.  Rod  to  be  heated,  with  support;  wax  or 
paraffine;  means  of  heating  the  rod.  Exp.  4.  Incandescent  lamp 
that  can  be  lighted.  Exp.  5.  Rods  of  wood,  glass,  and  iron,  with 
means  of  heating  them.  Exp.  6.  Rod  of  Exp.  1;  thin  glass  vessel; 
water;  means  of  heating.  Exp.  7.  Ring-stand;  lamp;  wire-gauze  or 
sand-bath;  water;  some  crystals  of  potassium  permanganate. 

OBJECT. — To  observe  what  happens  when  one  portion  of 
a  solid  is  kept  at  a  higher  temperature  than  the  rest. 

MANIPULATION. — The  rod  being  fastened  so  that  the 
end  to  be  heated  is  about  2  cm.  above  the  top  of  the  Bun- 
sen  burner,  close  the  air-holes  o*  the  burner,  light  it,  and 
turn  off  the  gas  until  the  flame  is  about  .5  cm.  high.*  Heat 
one  end  of  the  rod  with  this  low  flame,  and  record  your 
observations.  If  possible,  note  the  time  at  which  the  melt- 
ing of  each  piece  of  wax  begins.  Write  out  all  you  have 
learned  regarding  what  takes  place  when  a  portion  of  the 
rod  is  kept  at  a  higher  temperature  than  the  rest  of  the 
rod. 

EXPERIMENT  2. 

OBJECT. — To  study  the  distribution  of  the  heat  in  the 
rod. 

*  This  gives  the  yellow,  smoky  flame. 


HOW  HEAT  TRAVELS.  115 

MANIPULATION. — Remove  the  burner,  and  by  the  fingers 
or  any  convenient  method  test  the  temperature  at  different 
points  of  the  rod,  including  the  ends.  Draw  a  line  to  rep- 
resent the  rod,  and  illustrate  the  distribution  of  the  heat 
by  a  line  drawn  around  it. 

EXPERIMENT  3. 

OBJECT. — To  find  if  the  rod  loses  heat. 

MANIPULATION. — Replace  the  burner,  open  the  air-holes, 
turn  on  the  gas,  and  heat  one  end  of  the  rod  about  two 
minutes.  Remove  the  lamp  and  bring  your  hand  near,  but 
not  touching  the  end  that  was  heated.  Does  the  rod  seem 
to  be  losing  heat?  Is  this  loss  in  every  direction?  To 
test  this  latter  point,  hold  the  hand  about  .5  cm.  from  the 
heated  end  of  the  rod,  above,  below,  on  either  side,  and 
horizontally  from  the  end.  Write  out  what  you  have 
learned  regarding  the  loss  of  heat. 

EXPERIMENT  4. 

OBJECT. — To  observe  if  the  results  in  Exp.  3  can  still  be 
obtained  in  the  absence  of  air. 

MANIPULATION. — Observe  an  Edison  lamp  ;  turn  on  the 
current  and  see  if  the  heat  from  the  hot  carbon  reaches 
your  hand  through  the  space  in  the  globe  from  which  the 
air  has  been  exhausted.  Record  your  answer  to  the  ques- 
tion. 

EXPERIMENT  5. 

OBJECT. — To  find  if  all  bodies  behave  in  a  similar  man- 
ner when  one  portion  of  them  is  heated. 

MANIPULATION. — Repeat  Exp.  1  with  rods  of  wood,  iron, 
glass,  etc.,  recording  carefully  the  results  in  each  case.* 
See  if  you  can  class  together  any  substances  that  behave 
alike  in  this  respect.  Record  results  in  tabular  form. 

*  Or  the  experiment  can  be  tried  by  holding  one  end  of  the  rod  in 
the  hand,  heating  the  other  end  in  the  flame,  and  observing  whether 
tlie  end  in.  the  hand  bepoines  heated  or  notf 


116  HEAT. 

EXPERIMENT  6. 

OBJECT. — To  observe  what  happens  when  a  heated  body 
is  brought  in  contact  with  a  cooler  body. 

MANIPULATION. — Place  about  50  cu.cm.  of  water  in  a 
glass  vessel  and  note  the  degree  of  warmth  by  means  of  the 
finger.  Heat  one  end  of  the  copper  rod  for  a  few  moments, 
plunge  it  into  the  water,  stir  it  around,  withdraw  it,  and 
again  test  warmth  of  the  water.  State  your  inference. 

EXPERIMENT  7. 

OBJECT.— To  observe  what  happens  when  one  part  of  a 
liquid  is  heated  hotter  than  the  rest. 

MANIPULATION. — Support  the  thin  glass  vessel  used  in 
Exp.  6  on  a  ring-stand,  by  means  of  a  wire-gauze  ;  fill  it 
three-quarters  full  of  clean  water.  Have  ready  the  burner 
turned  down  low,  and  adjust  the  ring-stand  so  that  the 
vessel  is  supported  about  3  cm.  above  the  top  of  the  burner. 
Drop  into  the  water  four  crystals  of  the  pink  substance 
given  you  (which  in  dissolving  colors  the  water),  and  at 
the  same  instant  place  the  lamp  under  the  vessel.  Any 
motion  of  the  liquid  will  be  indicated  by  the  motion  of  its 
colored  portions.  Watch  carefully  and  draw  a  diagram 
representing  your  observations.  Compare  as  carefully  as 
possible  the  behavior  of  a  solid  with  that  of  a  liquid  when 
one  part  is  heated  more  than  another. 

Definitions. — The  process  by  which  heat  is  transferred 
from  one  part  of  a  body  to  another  part,  or  from  one  body 
to  another  in  contact  with  it,  is  called  Conduction.  The 
process  by  which  a  body  loses  heat  when  in  contact  with  no 
other  body,  as  in  the  case  of  the  electric  light,  is  called 
Radiation.  The  process  by  which  heat  is  distributed 
through  a  liquid  or  gas,  as  in  Exp.  7,  is  called  Convection. 
The  condition  of  a  body  as  regards  its  ability  to  give  up 
heat  is  called  its  Temperature.  The  body  giving  up  heat 
is  said  to  have  the  higher  temperature.  The  word  "tern- 


TESTING   THERMOMETERS.  117 

perature  "  is  used  to  indicate  the  relative  degree  to  which  a 
body  possesses  the  property  of  causing  the  sensation  that 
we  call  heat.  It  is  always  used  with  reference  to  the  con- 
dition of  some  other  body  taken  as  a  point  of  comparison. 

EXERCISE  2. 

TESTING  THERMOMETERS. 

Preliminary. — The  fact  that  bodies  expand  when  their 
temperature  is  raised  and  contract  when  it  is  lowered,  is 
made  use  of  in  constructing  instruments  to  measure  changes 
in  temperature.  These  instruments  are  called  thermome- 
ters. They  usually  consist  of  some  substance  so  arranged 
that  changes  in  its  volume  may  be  observed  on  a  scale. 
The  instrument  generally  used  in  laboratory  work  is  called 
a  chemical  thermometer.  The  substance  used  is  mercury. 
It  is  contained  in  a  glass  bulb  connected  with  a  fine  tube 
with  thick  walls.  The  scale  is  engraved  on  the  walls,  every 
ten  degrees  being  numbered.  The  centigrade  scale  is  gen- 
erally used.  At  the  top  of  the  instrument  is  a  small  glass 
eye  by  which  it  may  be  suspended.  Such  thermometers 
are  usually  provided  with  a  case  in  which  they  should 
always  be  kept  when  not  in  actual  use.  The  glass  of  the 
bulb  is  very  thin,  and  great  care  should  be  used  not  to 
break  it.  When  a  thermometer  is  used  to  determine  the 
temperature  of  a  liquid,  the  bulb  should  not  be  allowed  to 
come  in  contact  with  the  sides  or  bottom  of  the  containing 
vessel.  When  a  thermometer  has  been  at  one  temperature 
and  is  to  be  exposed  to  a  very  different  one,  as  in  changing 
from  ice-water  to  steam,  hold  it  in  the  air  a  moment  before 
exposing  it  to  the  new  temperature.  For  changes  of  a  few 
degrees  this  precaution  is  not  necessary.  In  reading  a 
chemical  thermometer,  a  white  card  held  behind  the  glass 
makes  the  position  of  the  top  of  the  mercury  column  much 
more  distinct. 


118  HEAT. 

After  thermometers  have  been  used  for  a  time,  the  posi- 
tion of  the  mercury  at  the  temperature  of  melting  ice  does 
not  always  agree  with  the  0  point  on  the  scale,  and  some- 
times the  position  at  100°  also  changes.  Hence  the  ther- 
mometer used  in  the  following  exercises  should  be  tested, 
in  order  that,  if  necessary,  corrections  may  be  made  in  its 
readings.  The  correctness  of  the  0  point  is  tested  by  plac- 
ing the  thermometer  in  melting  ice  (whose  temperature  is 
always  0);  the  100°  point  is  tested  by  immersing  the  ther- 
mometer in  steam  (whose  temperature  is  known).* 

EXPERIMENT. 

Apparatus.—  Thermometer  to  be  tested;  ice  or  snow;  water;  flask 
and  ring-stand,  and  wire-gauze  or  sand-bath;  tumbler;  clamp;  deliv- 
ery-tube; large  glass  tube  3  or  4  cm.  longer  than  thermometer,  corked 
at  one  end,  the  cork  having  a  hole  for  the  thermometer  and  another 
holding  a  piece  of  small  glass  tube  for  connecting  with  boiler. 

OBJECT. — To  test  the  correctness  of  the  points  on  the 
scale  of  the  thermometer  which  correspond  to  the  temper- 
atures of  melting  ice  and  steam. 

MANIPULATION. — Part  I.  Place  the  thermometer  in 
the  centre  of  some  pounded  ice  or  snow  in  a  tumbler,  the 
zero-pointf  on  the  scale  being  just  exposed.  Allow  it  to 
remain  there  until  the  mercury  has  ceased  to  fall.  Kecord 
the  point  on  the  scale  at  which  the  mercury  comes  to  rest. 
This  point  is  the  true  zero-point  on  the  scale. 

Part  II.  Clamp  the  large  tube  in  a  vertical  position, 
corked  end  up.  Connect  the  delivery-tube  from  a  flask 
about  two-thirds  full  of  water  with  the  small  tube  in  the 
cork.  Thrust  the  thermometer  through  the  other  hole  in 
the  cork  until  the  100°  point  is  just  above  the  cork.  Boil 
the  water  in  the  flask,  thus  surrounding  the  thermometer 

*  Of  course  thermometers  do  not  need  testing  every  year  or  with 
«?rery  class, 
f  These  instructions  assume  that  the  thermometer  has  a  centigrade 


TEMPERATURE  AND  PHYSICAL  FORM.         119 

with  steam,  and  note  the  reading  of  the  mercury  column 
when  it  comes  to  rest.  Draw  the  thermometer  up  until 
the  bulb  only  is  below  the  cork,  and  see  if  it  makes  any 
difference  in  the  reading  whether  all  the  mercury  is  heated 
or  not.  Read  the  barometer.  The  temperature  of  the 
steam  corresponding  to  the  atmospheric  pressure  may  be 
calculated  by  calling  the  temperature  corresponding  to  760 
mm.  100°,  and  adding  1°  for  each  27  mm.  above  760,  or 
subtracting  1°  for  each  27  mm.  below.  Record  the  ther- 
mometer-reading, the  true  temperature  of  the  steam,  and 
the  difference. 

EXERCISE  3. 

TEMPERATURE  AND  PHYSICAL  FORM. 

Preliminary. — We  already  know  that  when  the  tempera- 
ture of  a  solid  is  raised  sufficiently,  the  solid  changes  to  a 
liquid,  and  at  a  still  higher  temperature  to  a  gas.  That 
is,  the  physical  form  of  a  body  is  affected  by  its  tem- 
perature. In  the  following  exercise  we  wish  to  find 
out  all  we  can  about  what  goes  on  when  a  body  is 
heated.  Let  us  heat  a  body  and  note  its  changes  in 
temperature,  and  also  watch  for  any  other  changes.  Ice 
is  a  good  substance  to  work  with.  If  we  put  some  ice  in  a 
vessel,  heat  it,  and  note  the  temperature  at  regular  inter- 
vals, we  can  see  if  there  is  any  definite  connection  between 
temperature  and  physical  form.  At  the  beginning,  some 
water  must  be  added  to  the  ice  to  get  the  temperature,  as 
we  could  not  thrust  the  thermometer  directly  into  the  ice. 
The  contents  of  the  vessel  must  be  stirred  in  order  to  keep 
the  temperature  everywhere  the  same.  We  can  weigh  the 
vessel  before  and  after  heating  to  see  if  there  is  any 
change  in  weight.  The  apparatus  used  is  shown  in  Fig. 
70.  A  tin  pail  supported  over  the  burner  B.B.  is  filled 
with  ice  and  water.  The  temperature  is  measured  by  the 


120 


HEAT. 


thermometer  T,  and  the  contents  of  the  pail  stirred  by 
the  paddle  P. 


FIG.  70. 

EXPERIMENT. 

Apparat us.— Ring-stand  and  burner;  tin  pail;  paddle;  thermome- 
ter; ice  or  snow;  water;  watch  or  clock;  spring-balance  or  rough 
scales  ;  test-tube  of  cold  water  or  plate  of  clean  dry  glass. 

OBJECT. — To  observe  the  effects  of  heating  a  body. 

MANIPULATION. — Place  about  100  cu.  cm.  of  water  in 
the  pail;  add  enough  ice  or  snow  to  fill  the  pail  two-thirds 
full  of  the  mixture ;  weigh  the  pail  and  contents  on  the 


TEMPERATURE  AND  PHYSICAL  FORM.         121 

spring-balance.*  Record  the  weight.  If  ice  is  used,  it 
should  first  be  wrapped  in  a  cloth  and  pounded  until  it  is 
fine.  By  means  of  the  paddle  stir  the  contents  of  the  pail 
vigorously  until  the  thermometer  reads  zero.  Adjust  the 
thermometer  so  that  the  bulb  is  well  covered,  and  does  not 
touch  the  sides  or  bottom  of  the  pail.  Place  under  the 
pail  a  very  low  flame,,  turning  the  gas  nearly  off  and 
almost  closing  the  air  holes  in  order  to  prevent  backing- 
down.  Stir  vigorously,  taking  care  that  the  solid  and 
liquid  are  thoroughly  mixed,  and  being  careful  not  to 
break  the  bulb  of  the  thermometer.  Note  the  tempera- 
ture at  one-minute  intervals  until  four  minutes  after  the 
water  has  boiled.  The  readings  must  be  continuous  from 
the  beginning  to  the  end  of  the  experiment.  When  the 
readings  are  completed,  weigh  again.  From  time  to  time 
during  the  work  hold  over  the  pail  a  piece  of  clean  dry 
glass,  or  a  test-tube  filled  with  cold  water,  and  observe  the 
results.  In  addition,  note  all  that  goes  on,  and  record  all 
your  observations. 

Record  results  as  follows : 

Weight  before  = 

Weight  after     = 

TABLE  I. 


Time. 

Temperature. 

Remarks. 

Under  "Time,"  place  the  hour  and  minute  of  each 
reading.  Under  "  Temperature,"  place  the  thermometer- 
reading  to  0.1  degree.  Under  "Remarks,"  place  any 
observations  that  you  made  at  the  time  of  the  reading. 

*  A  64-oz.  balance  is  the  best. 


122 


HEAT. 


Note  carefully  changes  of  form,  appearance,  formation  of 
bubbles,  moisture,  etc. 

QUESTIONS. — 1.  What  effect  has  the  addition  of  heat  on 
the  physical  form  of  a  solid  ?  2.  What  effect  has  the  addi- 
tion of  heat  on  the  physical  form  of  a  liquid  ?  3.  Is  it 
possible  to  add  heat  to  a  body  and  not  raise  its  tempera- 
ture ?  4.  Under  what  circumstances  ?  5.  Under  what 
circumstances  does  the  addition  of  heat  raise  the  tempera- 
ture ?  6.  Is  any  change  of  weight  produced  ?  7  Why  is 
it  necessary  to  stir  the  mixture  ?  8.  When  the  tempera- 
ture rises,  is  the  rise  regular  ? 

GRAPHIC  REPRESENTATION  OF  RESULTS. 
CURVE  PLOTTING. 

Where  an  experiment  includes  two  sets  of  measure- 
ments, as  the  time  and  temperature  measurements  just 
made,  the  results  are  often  expressed  by  means  of  a  dia- 
gram. Suppose,  for  example,  the  following  data  have  been 
obtained : 


Time. 

Temp. 

Time. 

Temp. 

11  h.  3  m. 

5° 

11  h.  23m. 

4 

5 

7 

25 

3 

7 

4 

21 

2 

9 

3 

29 

4 

11 

3 

31 

5 

13 

5 

33 

6 

15 

8 

35 

5 

17 

6 

37 

4 

19 

7 

39 

3 

21 

5 

41 

0 

To  represent  these  results  in  a  diagram,  on  a  page  of 
of  your  note-book,  draw  two  lines  at  right  angles,  as  AB 
and  EC  in  Fig.  71.  Let  BO  represent  time  and  AB 
temperature.  Divide  the  line  BC  into  as  many  equal 
parts  as  there  are  observations  recorded  ;  in  this  case,  18. 


GRAPHIC  REPRESENTATION  OF  RESULTS.      123 


Divide  the  line  AB  into  as  many  equal  parts  as  there  are  de- 
grees between  the  highest  and  lowest  temperature  noted; 
in  this  case,  8.  From  each  of  the  points  a  draw  lines 
parallel  to  BC  and  equal  to  it  in  length,  and  from  the 
points  c  on  BC  draw  lines  parallel  to  AB,  thus  dividing 
the  paper  up  into  a  number  of  rectangles.  Starting  at 
the  point  where  the  two  lines  first  drawn  meet,  mark  on 


dddddddd 


d     d, 


7 


3      5 

n  (2) 


11  13  15  17  19  21  23  25  27  29  31 
FIG.  71. 


35  37  39 


AB  the  temperature  5,  the  first  observation,  by  making  a 
cross  five  spaces  up  the  line.  Then  on  the  next  vertical 
line,  which  marks  the  time  of  the  next  observation,  make 
a  cross  at  the  intersection  opposite  the  next  recorded  tem- 
perature. Proceed  in  this  way  until  all  the  temperatures 
have  been  entered.  Connect  the  centres  of  the  crosses  by 
straight  lines,  or  by  a  regular  curve.  The  line  so  obtained 
will  represent  the  temperature  at  various  times.  By  in- 
serting at  the  proper  places  on  the  curve  any  observations 


124 


HEAT. 


that  may  be  noted  as  regards  changes,  etc.,  a  complete 
graphic  account  of  the  results  of  the  experiment  is  ob- 
tained. This  process  is  called  curve-plotting,  and  is  much 
used  to  represent  to  the  eye  the  results  of  experiments. 

Taking  the  results  you  obtained  in  the  preceding  experi- 
ment, plot  a  curve  on  one  complete  page  of  your  note- 
book, representing  the  changes  in  temperature  during  the 
entire  experiment.  Enter  at  the  proper  points  of  the  curve 
any  phenomena  that  may  have  been  observed.  A  curve 
like  this  is  often  called  a  temperature-curve.  If  BC  be 
drawn  the  long  way  of  the  note-book  page,  the  blue-ruled 
lines  will  be  convenient  for  the  vertical  lines.  The  hori- 
zontal lines  should  be  ruled  very  lightly  with  a  pencil. 
Evidently  any  standard  of  length  can  be  used  in  laying  off 
the  spaces.  In  Fig.  71, 1  cm.  on  the  line  BC  represents  two 
minutes  of  Time,  and  2  cm.  on  the  line  AB  represent  one 
degree  of  Temperature  if  AB  =  16  and  BC  =  19  cm. 

EXERCISE  4. 

LAWS  OF  COOLING. 

EXPERIMENT. 

Apparatus.—  A  small  beaker-glass;  thermometer,  and  clamp  to 
support  it;  watch  or  clock ;  tin  pail;  water;  ring-stand;  and  burner 
for  heating  the  water. 

OBJECT. — To  observe  the  change  in  temperature  in  a 
cooling  body. 

MANIPULATION. — Place  about  50  cu.  cm.  of  hot  water  in 
a  beaker  glass,  suspend  the  thermometer  in  the  liquid,  and 
observe  the  temperature  every  minute  for  twenty  minutes. 
Every  five  minutes  also  observe  the  temperature  of  the 
room.  Record  results  as  follows: 


Temp. 

Time. 

Temp,  of  Room. 

Weight  used. 

Repeat  with  25  cu.  cm.  of  water. 


MELTING  AND  BOILING  POINTS.  125 

QUESTIONS. — 1.  What  have  you  observed  regarding  the 
changes  in  temperature  when  a  body  cools  ?  2.  Does  the 
quantity  of  the  body  make  any  difference?  3.  Plot  curves 
showing  the  changes  in  temperature  in  each  case.  4.  Does 
the  difference  in  temperature  between  the  body  and  the  air 
seem  to  affect  the  rate  at  which  the  temperature  falls  ? 

EXERCISE   5. 

MELTING  AND  BOILING  POINTS. 

Preliminary. — In  the  following  exercise  it  is  desired  to 
observe  the  melting-points  of  some  solids,  and  the  boiling- 
points  of   some  liquids.     The  melting-point  of  a  solid  is 
usually  determined  by  immersing  a  small  portion  of  it  in 
some  liquid  having  a  sufficiently  high  boiling-point,  heating 
the  liquid,  and  noting  its  temperature  when  the  solid  melts. 
For  bodies  which  it  is  supposed  will  melt  below  100°,  water 
is  used;   for  higher  melting-points,  other   liquids.      The 
solid  is  usually  placed  in  a  small  tube,  called  a 
melting -tube,  which  is  attached  alongside  the  ther- 
mometer.    A  melting-tube  is  made  by  drawing  out 
a  piece  of  glass  tubing  in  the  flame  of  a  Bunsen 
burner,  as  shown  in  Fig.  72.     The  tube  should  be 
about  10-15  cm.  from  the  narrow  neck  to  the  upper 
end,  and  the  small  part  about  3  cm.  long.     Melt 
some  of  the   solid    (paraffine,  for  instance)  in  a 
small  dish,  draw  a  little  up  into  the  tube,  and 
after   wiping  the   outside   allow   it   to   cool.      In    I 
determining  the  boiling-point  of  a  liquid,  a  test-   FIG.  72. 
tube,  containing  about  1  cu.  cm.  of  the  liquid  takes  the 
place  of  the  melting-tube. 

EXPERIMENT    1. 

Apparatus.—  Ring-stand;  sand-bath  and  burner;  thermometer,  and 
some  means  of  supporting  it;  "  melting-tubes;"  wax  or  paraffine  in 
small  dish  (if  tubes  are  unprepared);  water;  stirring-rod;  rubber 
bands. 

OBJECT. — To  determine  the  melting-point  of  a  solid. 
MANIPULATION. — Attach  the  tube  containing  the  solid 


a 


126 


SEAT. 


to  the  thermometer  by  elastic  bands  or  strings,  as  indicated 
in  Fig.  73,  the  solid  being  on  a  level  with  the  thermometer 
bulb,  and  support  the  whole  so  that  the  bulb  is  about  in 
the  centre  of  the  dish  of  water.  Heat  the  water  slowly, 
stirring  gently,  and  note  the  temperature  either  when  the 
solid  becomes  transparent,  or  when  it  slides  up  the  tube. 
Either  of  these  may  be  taken  as  indicating  the  melting- 
point.  The  second  gives  a  little  higher  temperature  than 
the  first.  Add  some  cold  water,  and  repeat  with  a  fresh 
tube.  If  possible,  try  more  than  one  substance. 
T 


FIG.  73. 


FIG.  74. 


EXPERIMENT    2. 

OBJECT. — To  determine  the  boiling-point  of  a  liquid. 

MANIPULATION". — Place  about  1  cu.  cm.  of  the  liquid  in 
a  test-tube  and  support  the  tube  in  the  beaker,  which  has 
been  filled  with  cold  water,  so  that  the  liquid  is  in  the 
centre  of  the  water,  as  in  Fig.  74.  Warm  the  water  slowly, 


BEAT  CAPACITY.  127 

stirring  gently  with  the  thermometer,  and  note  the  tem- 
perature at  which  the  liquid  begins  to  boil.  It  is  best  to 
shake  the  tube  gently  while  heating.  Make  two  deter- 
minations with  one  liquid,  and,  if  possible,  repeat  with 
another  liquid.  Alcohol,  ether,  etc.,  are  very  inflammable, 
and  should  be  kept  away  from  the  fire. 

EXERCISE   6. 

HEAT  CAPACITY. 

Preliminary. — In  the  following  exercise  we  wish  to  study 
the  conditions  affecting  the  rise  in  temperature  of  bodies 
when  heated.  We  already  know  that  the  longer  a  body  is 
heated,  the  more  its  temperature  rises,*  provided  no  change 
of  form  takes  place,  and  that  the  greater  the  difference  in 
temperature  between  the  source  of  heat  and  the  body,  the 
more  rapid  will  be  the  change. f  In  the  following  exercise 
we  wish  to  see  if  the  nature  and  quantity  of  the  body 
heated  have  any  effect.^ 

EXPERIMENT. 

Appara tits.— Part  I:  Test-tube,  with  perforated  cork;  thermom- 
eter; tin  pail;  ring-stand;  burner;  water;  scales  and  weights;  a  bu- 
rette or  graduated  cylinder. 

Part  II.:  Three  test-tubes  with  corks;  mercury;  alcohol;  empty 
tumbler;  also  the  apparatus  for  Part  I. 

OBJECT. — To  observe  the  effect  on  the  rise  of  tempera- 
ture in  a  body  produced  by  (a)  quantity,  (b)  material. 

MANIPULATION.— Part  I.  Effect  of  Quantity :— Place  4 
grams  of  water  in  the  test-tube,  close  the  mouth  of  the  tube 
by  a  cork  through  which  the  thermometer  passes,  the  bulb 
being  immersed  in  the  liquid.  Have  ready  the  large  vessel  in 
which  the  water  is  about  50°,  place  the  tube  in  the  water,  stir 
it  gently,  and  observe  the  time  required  for  the  thermom- 

*  Ex.  3.  f  Ex.  4. 

\  Let  each  pupil  prepare  a  statement  of  the  conditions  under  which 
such  an  exercise  must  be  conducted. 


128 


BEAT. 


eter  to  rise  10  degrees.     Repeat  the  experiment  with  twice 
the  weight  of  water. 

Part  II.  Effect  of  Material : — Weigh  out  in  three  tubes 
15  grams,  respectively,  of  water,  mercury,  and  alcohol. 
Cork  the  tubes,  and  stand  them  upright  in  an  empty 
tumbler  until  ready  for  use.  Take  the  tube  containing  the 
water  and  substitute  for  its  cork  the  one  bearing  the  ther- 
mometer. Having  the  thermometer  bulb  immersed  in  the 
water,  read  the  temperature  of  the  liquid  and  then  plunge 
it  into  the  heated  water.  Shake  it  gently,  and  observe  the 
time  required  for  the  thermometer  to  rise  2  degrees.  Re- 
peat the  experiment  with  the  other  liquids.  Tabulate  the 
results  as  follows : 


Wt.  used. 

Original  Temp. 

Final  Temp. 

Time  of  Immersion. 

Body. 

QUESTIONS. — 1.  For  a  given  substance,  can  you  make 
out  any  relation  between  the  rise  of  temperature  and  the 
weight  used  ?  2.  Will  exposure  to  the  same  temperature 
for  the  same  time  cause  the  same  rise  in  temperature  in  all 
bodies  ? 

EXERCISE  7. 

DETERMINATION  OF  SPECIFIC  HEAT. 

Preliminary. — We  observed  in  the  preceding  experiment 
that  when  equal  weights  of  various  bodies  were  exposed  to 
the  same  temperature  for  the  same  time,  the  temperature 
of  some  rose  more  rapidly  than  that  of  others.  This  is  in- 
dicated by  saying  that  they  have  different  heat  capacities. 
The  lower  the  heat  capacity,  the  higher  the  temperature 
rose;  and  the  less  the  temperature  rose,  the  greater  the 
heat  capacity.  Which  has  the  greater  heat  capacity — water 
or  mercury? 


DETERMINATION  OF  SPECIFIC  HEAT.          129 

The  unit  of  heat  quantity  is  the  heat  required  to  raise  a 
unit  of  weight  of  water  from  0  to  1°  on  a  temperature  scale- 
hence  the  quantity  of  heat  taken  by  any  quantity  of  water 
is  found  by  multiplying  the  weight  of  the  water  by  its  rise 
in  temperature,  or 

H=  W  X  Rise  in  temp. 

Evidently  we  can  have  several  units  of  heat,  according  to 
the  unit  of  weight  taken  and  the  thermometer  scale  used. 
The  units  of  weight  generally  used  are  metric,  the  kilo- 
gram and  the  gram,  and  the  scale  used  is  the  centigrade. 
The  corresponding  unit  of  heat  is  called  the  calorie.  When 
kilograms  are  used  the  calorie  is  designated  by  a  capital  C\ 
when  grams  are  used,  by  a  small  c. 

In  order  to  be  able  to  use  these  heat-units  for  all  bodies, 
we  must  compare  their  heat  capacities  with  that  of  water, 
which  is  taken  as  the  standard.  This  comparison  is  ex- 
pressed as  the  ratio  of  the  heat  capacity  of  the  body  to 
that  of  water,  and  this  ratio  is  called  the  Specific  Heat 
of  the  body.  As  the  specific  gravity  of  a  body  expresses 
how  many  times  its  density  is  that  of  water,  so  the  specific 
heat  of  a  body  expresses  how  many  times  its  heat  capacity 
is  that  of  water. 

The  simplest  way  to  determine  specific  heat  would  be  to 
take  equal  weights  of  water  and  the  body  to  be  tested, 
expose  them  for  the  same  length  of  time  to  the  same  tem- 
perature, and  note  the  rise  of  temperature.  The  higher 
the  temperature  of  the  body  rose,  the  less  would  be  its  heat 
capacity.  If,  for  example,  the  temperature  of  the  body 
rose  twice  as  much  as  that  of  the  water,  its  capacity  would 
be  half  as  much,  and  its  specific  heat  one  half;  if  it  rose 
half  as  much,  its  specific  heat  would  be  2,  etc.  Calculate 
from  the  data  of  the  preceding  exercise  the  specific  heat 
of  mercury. 


130  HEAT. 

Specific  heat  is  usually  determined  by  what  is  called  the 
"method  of  mixture."  This  consists  in  heating  the  body 
to  a  known  temperature,  and  then  bringing  it  in  contact 
with  water  in  a  vessel,  called  a  calorimeter,  which  will  not 
lose  heat  by  radiation.  The  body  will  lose  heat  and  the 
water  will  gain  it,  until  both  are  at  the  same  temperature. 
Then  the  quantity  of  heat  gained  by  the  water  will  equal 
the  quantity  of  heat  lost  by  the  body.  If  we  know  the 
weight  of  water  in  the  calorimeter,  and  how  many  degrees 
it  was  raised,  we  can  calculate  how  much  heat  was  gained 
by  the  water,  or,  the  equivalent,  that  lost  by  the  body.  If 
we  also  know  the  weight  of  the  body,  and  the  number  of 
degrees  it  cooled,  we  can  determine  how  many  heat-units 
would  be  given  out  by  one  gram  of  the  body  cooled  1°. 
Dividing  this  by  the  amount  of  heat  that  would  be  given 
off  by  one  gram  of  water  cooled  1°,  we  can  get  the  specific 
heat.  In  the  following  exercise  we  use  an  iron  ball  of 
known  weight,  heated  in  boiling  water  to  100°.  Taking  a 
known  weight  of  water  and  noting  the  rise  in  temperature, 
we  calculate  the  specific  heat. 

EXPERIMENT. 

Apparatus.— Body  whose  specific  heat  is  to  be  determined.  Tin 
pail;  ring-stand  and  burner;  water;  thermometer  with  white  card; 
scales  and  weights;  calorimeter;  three  corks;  thread. 

OBJECT. — To  determine  the  specific  heat  of  a  given  solid. 

MANIPULATION. — Fill  the  pail  about  three-fourths  full 
of  water,  and  light  the  burner  under  it.  Weigh  the  calo- 
rimeter, fill  it  about  two-thirds  full  of  water,*  and  weigh 

*  The  point  is  iiot  to  get  so  much  water  in  the  calorimeter  that  it 
will  overflow  when  the  body  is  put  in,  but  yet  to  have  enough  to 
completely  cover  it.  A  preliminary  trial  may  be  needed.  Place  the 
body  in  the  calorimeter,  and  then  add  water  enough  to  fill  the  calo- 
rimeter to  about  5  cm.  of  the  top.  On  withdrawing  the  body,  the 
amount  of  water  for  good  working  conditions  remains,  and  may  be 
weighed. 


DETERMINATION  OF  SPECIFIC  HEAT.  131 

again.  Support  the  calorimeter  on  the  corks  upon  the 
table  at  some  distance  from  the  heating  apparatus,  and  put 
the  thermometer  into  it.  Weigh  the  solid  under  examina- 
tion. When  the  water  in  the  pail  boils,  suspend  the  solid 
in  the  centre  by  means  of  a  thread,  and  allow  it  to  remain 
there  until  it  has  assumed  the  temperature  of  the  water 
(100°  approximately).  This  will  take  about  four  minutes. 
Then  read  the  thermometer  and  quickly  transfer  the  solid 
to  the  calorimeter.  Stir  gently  with  the  thermometer 
and  read  it  to  0.2  at  intervals  of  half  a  minute  (record 
these  readings)  until  the  temperature  of  the  water  begins 
to  fall.  The  highest  reading  of  the  thermometer  is  the 
temperature  to  which  the  solid  heats  the  water.  If  time 
allows,  repeat  with  different  quantities  of  water  in  the 
calorimeter.  Record  results  as  follows: 

Weight  of  body  = 

Calorimeter  -+-  water  = 
Calorimeter  alone       = 

Water  alone 

Temperature  of  body  before  immersion  = 

"         "  water  in  cal.  after  body  is  in     = 
"        "      "     "    "  before  body  was  in  = 


Increase  in  temp,  of  water  in  calorimeter  = 

Fall  in  temp,  of  body  = 

QUESTIONS. — Explain  why  the  space  between  the  walls 
of  the  calorimeter  is  filled  with  excelsior.  Suggest  some 
other  substances  that  would  do  as  well.  Why  should  the 
solid  be  suspended  by  a  thread  rather  than  by  a  wire? 
What  error  is  introduced  by  doing  so  ?  What  error  is  in- 
troduced in  calling  the  original  temperature  of  the  ball 
100°? 


132  HEAT. 

CALCULATION.— Call  the  weight  of  the  body  W  and  the 
weight  of  water  in  the  calorimeter  W,  the  original  tempera- 
ture of  the  water  t  and  the  final  temperature  t' .  Then  W 
grammes  of  the  body  in  cooling  from  100°  to  t'  degrees 
gave  off  sufficient  heat  to  raise  W  grammes  of  water  from 
t  degrees  to  t'  degrees,  or  raised  it  t'  —  t  degrees;  the 
amount  of  heat  given  up  was 

WX  (t'-t). 

As  the  heat  was  given  up  by  W  grammes  of  the  body 
cooled  from  100°  to  t'  degrees,  the  amount  of  heat  given 
out  by  one  gram  cooled  one  degree  was 

W  X  (t'  -  t) 
W'X  (100-*')" 

Since  this  also  represents  the  amount  of  heat  that  would 
be  required  to  raise  one  gram  of  the  body  1°,  we  can  get 
the  specific  heat  of  the  body  by  dividing  this  value  by  the 
amount  of  heat  that  would  be  required  to  raise  1  gram  of 
water  1°  or  \c\  so 

W  X  (tf  -  t) 

.,    ,               W  X  (100  -  t') 
Specific  heat  =  ^ '—. 

j-C 

By  substituting  in  this  equation  the  values  obtained  in  the 
experiment,  the  specific  heat  of  the  body  may  be  calculated. 
In  this  calculation  we  have  neglected  to  take  into  ac- 
count the  heat  that  went  into  the  calorimeter,  which  was 
itself  heated.  To  make  this  correction,  weigh  the  vessel 
that  formed  the  inside  of  the  calorimeter.*  This  gives 
the  weight  which  was  heated  from  the  original  tempera- 
ture of  the  water  to  its  final  temperature,  or  t'  —  t\  and 
so  the  heat  that  went  into  the  calorimeter  =  Wt.  cal.  X  t9 
—  t  X  the  specific  heat  of  the  material  of  the  calorimeter.! 

*  Or,  if  a  metallic  calorimeter  be  used,  weigh  the  whole  vessel, 
f  Glass,  0.198;  brass,  0.858;  iron,  0.1124. 


LATENT  HEAT.  133 

The  total  heat  given  out  by  the  body  equals  that  which 
went  into  the  water  plus  that  which  went  into  the  calorim- 
eter. The  corrected  formula,  then,  would  be: 

SPECIFIC  HEAT  = 

[W  X  (f  —  t)]  +  [wt.  cal.  X  (f  —  t)  X  sp.  heat  of  cal.] 
W  '  X  (100  -  t') 


Re-calculate  your  value  for  specific  heat  with  the  correction 
for  the  calorimeter. 

EXERCISE   8. 

LATENT  HEAT. 

Preliminary.  —  The  name  latent  heat  is  given  to  the  heat 
which  is  required  to  change  a  solid  to  a  liquid,  or  a  liquid 
to  a  gas,  without  altering  its  temperature.  Latent  heat 
is  usually  determined  (1)  by  measuring  the  heat  given 
out  by  a  known  weight  of  vapor  at  the  boiling-point  of 
the  liquid  when  condensed  at  that  point,  or  (2)  by  deter- 
mining the  heat  absorbed  by  a  known  weight  of  the  solid 
at  the  melting-point  when  changed  to  a  liquid  at  that  tem- 
perature. In  this  exercise,  the  number  of  heat-units  given 
off  by  one  gram  of  steam  at  100°  when  changed  to  water  at 
that  temperature  is  to  be  ascertained.  The  steam  is  con- 
densed under  such  conditions  that  the  heat  given  off  will 
raise  the  temperature  of  a  known  weight  of  water.  If  we 
know  the  weight  of  steam  condensed,  the  weight  of  water 
heated,  and  the  number  of  degrees  that  it  was  raised  by  the 
condensed  steam,  we  can  calculate  the  latent  heat. 

The  apparatus  used  in  the  first  method  consists  of  a  glass 
vessel  Dy  Fig.  75,  holding  the  water,  and  containing  a  glass 
coil  E,  which  terminates  in  a  tube  that  projects  from  the 
bottom  of  the  vessel.  This  coil  is  connected  by  the  tube  C 
with  the  flask  A,  which  furnishes  steam.  K  is  an  arrange- 
ment to  prevent  any  condensed  steam  from  passing  into 


134 


HEAT. 


the  coil.  The  tube  C  is  thickly  wound  with  cloth  to  stop 
any  loss  of  heat  and  resulting  condensation  of  steam  before 
reaching  E.  When  steam  from  A  reaches  E  it  condenses, 


FIG.  75. 

and  so  raises  the  temperature  of  the  water  in  D.  The  con- 
densed steam  runs  out  into  a  vessel,  and  the  weight  of 
water  so  formed  gives  us  the  weight  of  steam  condensed. 

EXPERIMENT  1  . 

Apparatus.— Ring-stand ;  wire-gauze;  burner;  small  beaker-glass; 
scales  and  weights;  thermometer;  liter  and  half-liter  flasks;  paddle; 
apparatus  as  in  Fig.  75. 

OBJECT. — To  determine  the  number  of  heat-units  re- 
quired to  change  one  gram  of  steam  at  100°  to  water  at 
100°. 

MANIPULATION. — Fill  the  flask  A  about  two-thirds  full 
of  water  and  set  it  to  boiling,  the  delivery-tube  being  dis- 
connected at  H.  Place  a  measured  quantity  of  water  in 
D  *  (2  to  4  liters,  according  to  size),  and  suspend  the  ther- 

*  The  object,  of  course,  is  to  get  a  known  weight  of  water  in  D. 
This  could  be  done  by  weighing  D,  filling  it  with  water,  and  weigh- 
ing it  again.  It  is  much  more  convenient,  however,  to  measure  the 


LATENT  HEAT.  135 

mometer  in  the  liquid.  As  1  cu.  cm.  of  water  =  1  gram, 
you  now  know  the  weight  of  water  in  D.  Weigh  the  small 
glass  vessel  F.  When  "live  steam"  comes  out  of  the  de- 
livery-tube at  H,  connect  it  with  the  glass  coil  and  allow  it 
to  run  for  three  minutes,  meantime  stirring  the  water  in 
D  with  the  paddle.*  Eead  the  temperature  of  the  water 
in  D,  and  immediately  place  the  small  glass  vessel  under 
the  end  of  the  glass  coil  to  catch  the  distilled  water.  "  Let 
the  apparatus  run  from  15  to  20  minutes,  stirring  the 
water  in  D  gently  all  the  time;  then  remove  the  glass  ves- 
sel containing  the  condensed  steam,  and  immediately  read 
the  temperature  of  the  water  in  D.  Disconnect  the  steam- 
pipe  and  turn  out  the  gas  under  A.  Weigh  the  vessel 
containing  the  condensed  steam.  Arrange  the  results  afc 
follows: 

Water  in  the  condenser  = 

Original  temperature      = 

Final  temperature  = 

Kise  in  temperature       = 

Vessel  -j-  condensed  steam     = 
Vessel  alone  = 

Weight  of  steam  condensed  = 

CALCULATION.— Call  JFthe  weight  of  water  in  the  con- 
denser, W  the  weight  of  steam  condensed,  t  the  original 
temperature  of  the  water  in  /),  and  t'  the  temperature  to 
which  it  was  raised.  Then  W  X  (tf  —  t)  =  the  heat  gained 

water.  It  is  best  to  fill  D  within  about  5  cm.  of  the  top,  and  it  is 
convenient  to  take  a  volume  which  can  be  measured  by  liter  or 
half -liter  flasks. 

*  In  stirring,  care  should  be  used  not  to  break  the  glass  coil,  and 
to  continually  stir  the  water  up  from  the  bottom,  at  which  point  the 
colder  water  will  always  collect.  The  thorough  stirring  of  the  water 
js  an  important  point  all  through  the  experiment. 


136  HEAT. 

by  the  water  in  D  during  the  experiment.  This  amount  of 
heat  includes  not  only  the  heat  given  out  by  the  steam  at 
100°  when  condensed  to  water  at  100°,  but  also  the  heat 
given  out  by  the  water  so  formed  in  cooling  from  100°  to 
the  temperature  of  the  water  in  Z>,  which  varied  from  t 
degrees  at  the  beginning  to  tf  degrees  at  the  end  of  the 
experiment.  The  average  temperature  to  which  this  water 

/'  4-  t 
was  cooled  was  —  -  —  »  and  the  amount  of  heat  given  off  by 

6 

the  water  formed  from  the  steam  in  cooling  was  * 

W  x  (100  -  £ 

So  that  the  heat  gained  due  to  the  condensation  of  steam 
alone  is 


[Wx(f-  1)]  -  [w  x  (100  -  ^J-)], 

and  the  amount  of  heat  per  gram  is 

[Tf  X  (t'  -  t)]  -  [V  X    lOO  - 


W 

There  are  two  errors  that  still  need  correcting  for,  if  the 
results  are  to  be  at  all  accurate.  (1)  The  glass  vessel  D 
and  the  glass  coil  E  are  raised  from  t  degrees  to  t'  degrees, 
as  well  as  the  water  inside;  hence  the  value  taken  for  the 
heat  given  out  is  too  small  by  the  amount  that  went  into 
the  glass.  To  correct  for  this,  weigh  D  and  the  coil  to- 
gether. Calling  this  weight  G,  the  heat  that  went  into  the 

*  The  original  temperature  being  100°,  the  average  fall  in  tempera- 
ture would  be  100° ~~. 

& 


LATENT  HEAT. 


137 


glass  is  G  X  (f  —  f)  X  specific  heat  of  glass.*  If  this 
quantity  be  added  to  the  value  taken  before  for  the  heat 
given  up  to  D,  it  will  give  more  accurate  results.  (2)  Dur- 
ing the  experiment  the  water  in  D  was  losing  heat  to  the  air 
in  the  room.f  This  error  can  be  avoided  by  filling  D  with 
water  a  number  of  degrees  below  the  temperature  of  the 
room,];  and  stopping  the  experiment  when  it  is  heated  as 
much  above  the  temperature  of  the  air  as  it  started  below. 
Then  the  water  in  D  takes  as  much  heat  from  the  air  while 
below  its  temperature  as  it  gains  while  above,  and  so  this 
error  cancels  out.  The  corrected  calculation,  then,  is 

LATENT  HEAT  = 

[Gx(t'-t)  X  sp.  heat  glass]  -f  [Wx  (<'-<)]- 


W  X 


-~-\  I 


SUBSTITUTE  EXPERIMENT. 

Preliminary.  —  The  apparatus  is  shown  in  Fig.  76.  Steam 
is  generated  in  the  flask,  and  passes  through  the  covered 
tube  into  the  calorimeter  contain- 
ing a  known  weight  of  water.  The 
temperature  of  this  water  is  ob- 
served before  and  after  running  in 
steam,  and  the  increase  in  weight  of 
the  calorimeter  gives  the  weight  of 
steam  condensed.  The  tube  is  cov- 
ered with  cloth  to  prevent  conden- 
sation. The  calorimeter  is  sup- 
ported on  a  block  or  box,  so  that  FIG.  76. 

by  removing  the  support,  the  calorimeter  can  be  quickly 

*  This  may  be  taken  as  0.198. 

f  For  another  method  of  correcting  for  this  error,  see  Worthing- 
ton,  p.  190. 

t  This  can  usually  be  done  by  taking  water  from  the  faucet  after 
letting  it  run  awhile,  where  there  is  a  water  service;  otherwise,  a 
little  ice  or  snow  may  be  added. 


138  HEAT. 

dropped  down  so  as  to  clear  the  end  of  the  delivery-tube 
without  disturbing  the  flask. 

Apparatus. — Ring-stand;  wire-gauze;  burner;  flask  with  cork 
and  delivery-tube;  scales  and  weights;  calorimeter  and  thermom- 
eter with  white  card;  support  for  calorimeter  (books,  block  of 
wood  or  small  box). 

OBJECT. — To  determine  the  amount  of  heat  given  out 
by  one  gram  of  steam  at  100°  in  condensing  to  water  at 
100°. 

MANIPULATION. — Weigh  the  vessel  to  be  used  as  a  calo- 
rimeter, add  about  300  cu.  cm.  of  water,  weigh  again,  and 
place  the  thermometer  in  the  vessel.  Fill  the  flask  two- 
thirds  full  of  water  and  heat.  After  the  steam  has  escaped 
freely  from  the  delivery-tube  for  three  or  four  minutes,  note 
the  temperature  of  the  water  in  the  calorimeter,  and  as 
quickly  as  possible  plunge  the  delivery-tube  nearly  to  the 
bottom  of  it.  While  the  steam  is  condensing,  stir  gently 
with  the  thermometer,  noticing  the  temperature  from  time 
to  time.  When  the  temperature  of  the  water  in  the  calo- 
rimeter is  8°  or  10°  above  that  of  the  room,  withdraw  the 
delivery-tube  as  rapidly  as  possible,  and  remove  the  lamp 
from  beneath  the  flask.  Note  the  temperature  of  the  water 
in  the  calorimeter,  and  weigh  the  latter.  Eecord  the  re- 
sults as  follows: 

Calorimeter  -f  water  =  Steam  condensed  = 

"  =  Temp,  before 

Water  Temp,  after 

Calorimeter  +  water  after    =  Gain  in  temp.       = 
Calorimeter  +      "    before  = 

EXERCISE  9. 

COEFFICIENT  OF  LINEAR  EXPANSION. 

Preliminary. — We  know  that  when  a  body  is  heated  it 
expands.  The  fraction  of  its  length  at  0  that  it  expands 


COEFFICIENT  OF  LINEAR  EXPANSION.          139 

when  heated  1°  is  called  its  coefficient  of  linear  expansion, 
or  the  linear  coefficient  of  expansion.  The  fraction  of  its 
bulk  at  0  that  it  expands  when  heated  1°  is  called  its  coeffi- 
cient of  cubical  expansion,  or  the  cubical  coefficient  of  expan- 
sion. Evidently  fluids  would  have  no  coefficient  of  linear 
expansion,  but  solids  would  have  both.*  In  the  following 
exercise  we  wish  to  determine  the  average  linear  coefficient 
of  a  metallic  rod. 

First  Method.  The  apparatus  is  shown  in  Fig.  77.  The 
rod  c  is  surrounded  by  a  large  tube  ee,  which  is  first  filled 
with  ice-water  and  then  with  steam,  thus  heating  the  rod 


FIG.  77. 


100°.  The  changes  in  length  are  magnified  by  the  lever 
p,  which  reads  on  the  scale  S.  In  this  way  we  can  meas- 
ure the  change  in  length  of  the  rod  when  heated  from  0  to 
100°  and  determine  the  required  coefficient. 


*  Suggestion:   Give  the  principles  on  which  such  measurements 
would  be  based. 


140 


EXPERIMENT  1. 

Apparatus. — As  shown  in  Fig.  77.     Also,  water;  ice;  funnel;  tin 
pail;  meter-stick;  flask;  ring-stand;  burner;  connecting  tubes. 

OBJECT. — To  determine  the  linear  coefficient  of  expan- 
sion of  a  solid. 

MANIPULATION. — The  chief  error  in  this  experiment  is 
in  the  determination  of  length,  since  only  the  part  of  the 
rod  inside  the  corks  is  at  exactly  the  measured  tempera- 
tures, though  the  rest  of  it  becomes  heated  by  conduction 
and  expands  to  some  extent.  If  we  take  the  length  be- 
tween the  outsides  of  the  corks,  we  shall  come  very  near 
the  truth. 

To  get  the  length  at  zero.  Attach  the  glass  funnel  to 
the  rubber  tube  L,  place  a  vessel  under  the  exit-tube  A", 
and  pour  ice-water  through  the  apparatus  until  the  ther- 
mometer T  has  read  zero  for  several  minutes.  Read  care- 
fully the  position  of  the  pointer  on  the  scale,  and  measure 
the  length  of  the  rod  between  the  outsides  of  the  corks. 
Allow  the  water  to  run  out.  Connect  with  the  flask  F, 
and  run  steam  through  the  apparatus  until  the  pointer 
again  comes  to  rest;  then  note  its  position.  If  time  allows, 
again  pour  ice- water  through,  and  see  if  the  pointer  comes 
back  to  its  first  position.  If  so,  repeat  the  experiment;  if 
not,  record  the  fact. 

To  find  increase  in  length.  By  means  of  compasses, 
measure  carefully  the  distance  between  the  two  pivots,  re- 
peating several  times,  and  recording  each  measurement. 
Measure  also  the  distance  from  the  lower  pivot  to  the  point 
on  the  needle  at  which  you  took  your  reading.  The  aver- 
age length  of  the  "long  arm"  divided  by  the  average  length 
of  the  "short  arm"  gives  the  magnifying-power  of  the 
pointer.  Record  results  as  follows: 

Length  of  rod  = 

Mag. -power  of  the  pointer  = 


COEFFICIENT  Off  LINE  AH  EXPANSION.         141 

TABLE   OF   MEASUREMENTS. 

1st  Trial.        2d.  3d.        Av. 
Short  arm, 
Long  arm, 

Magnify  ing-power  = 

Reading  pointer  at  0  = 

"  "       "  100  = 

Increase  on  pointer  = 

True  increase  = 

Coefficient  — 

CALCULATION". — Substract  the  smaller  reading  of  the 
pointer  from  the  larger;  this  gives  the  space  traversed 
by  the  pointer.  This,  divided  by  the  magnifying-power  of 
the  pointer,  gives  the  true  increase  in  the  length  of  the 
rod.  This  increase,  divided  by  the  length  of  the  rod  at 
zero,  gives  the  coefficient  of  linear  expansion  as  a  decimal 
which  is  to  be  carried  out  to  the  fourth  place  of  significant 
figures.  Or,  calling  L  the  length  of  rod  at  0,  M  the  mag- 
nifying-power of  the  pointer,  S  the  reading  of  the  pointer 
at  0,  S'  the  reading  of  the  pointer  at  100, 

Increase,  100°  =  8'  ~  S 


Increase,  1°     = 


Linear  coefficient  of  expansion  = 


M 

S'  -  S  a 
MX  ioo; 

8' -8 
M  X  100* 


Second  Method.     The  apparatus  used  is  shown  in  Fig. 
78.     The  rod  is  inside  the  tin  jacket  R,  which  can  be  filled 


142 


HEAT. 


with  either  steam  or  ice-water,  thus  changing  the  tempera- 
ture of  the  rod  100°.  For  measuring  the  increase  in 
length,  the  pointer  P,  moving  on  the  clock  face,  is 
attached  to  a  screw,  D,  which  advances  a  known  distance 
for  each  turn.  The  end  of  this  screw  is  in  line  with  the 
end  of  the  rod,  and  the  screw  is  connected  with  one  wire 


FIG.  78. 

leading  from  a  source  of  electricity,  while  the  rod  is  con- 
nected with  the  other  wire.  When  the  end  of  the  screw 
touches  the  end  of  the  rod  the  circuit  is  completed,  and 
this  fact  is  indicated  by  some  instrument  placed  in  the 
circuit.  If  we  know  how  far  the  screw  advances  at  one 
turn,  the  change  in  length  of  the  rod  may  be  very  accu- 


COEFFICIENT  OF  LINEAR  EXPANSION.      143 

rately  measured  by  finding  how  many  turns  of  the  screw 
move  its  end  enough  to  make  contact  with  the  end  of  the 
rod  first  at  0  and  then  at  100°. 

EXPERIMENT  2. 

Apparatus.—  As  shown  in  Fig.  78.  Also,  ice-water;  tumbler;  meter- 
stick;  boiler,  burner,  and  ring  stand;  current  of  electricity  and  some 
instrument  to  indicate  when  the  circuit  is  completed  (galvanometer; 
lamp;  sounder). 

OBJECT. — To  determine  the  linear  coefficient  of  expan> 
sion  of  a  metallic  rod. 

MANIPULATION. — Arrange  the  apparatus  as  in  Fig.  78, 
connecting  the  glass  vessel  V  with  the  jacket  R,  as 
shown.  Turn  the  pointer,  P,  until  the  end  of  the  screw, 
D,  is  just  in  contact  with  the  end  of  the  rod.  Place  a 
vessel*  under  the  end  of  the  exit-tube,  fill  V  with  ice- 
water,  and  allow  it  to  run  through  the  jacket,  thus  sur- 
rounding the  rod  with  water  at  0.  As  the  rod  contracts, 
turn  the  pointer  so  as  to  just  keep  contact  between  the  end 
of  the  screw  and  the  end  of  the  rod,  and  continue  until 
there  is  no  further  change  in  length.  During  this  time 
keep  ice-water  constantly  running  through  the  jacket. 
When  the  rod  has  ceased  to  contract,  read  the  position  of 
the  pointer  at  which  the  end  of  the  screw  just  touches  the 
end  of  the  rod,  and  turn  the  pointer  back  half  a  revolu- 
tion or  so.  Replace  V  by  a  flask  two-thirds  full  of  water, 
and  connect  it  with  the  jacket  R.  With  a  Bunsen  burner 
heat  the  flask  and  pass  the  steam  through  the  jacket. 
During  this  operation  turn  the  pointer  back  as  fast  as 
contact  is  made  by  the  expansion  of  the  rod.  The  expan- 
sion will  be  very  rapid.  When  the  rod  has  ceased  to  ex- 
pand, note  the  position  of  the  pointer  at  which  contact  is 
just  made,  and  record  the  total  number  of  minutes  on  the 

*  When  this  vessel  is  full,  the  contents  are  to  be  poured  back  into 
V.  It  is  well  to  have  a  little  ice  in  it  to  hold  the  temperature  of  the 
water  at  0. 


144  BOAT. 

clock  face  which  the  pointer  was  turned  back  from  its  po- 
sition when  the  rod  was  at  0.  This  number,  multiplied  by 
the  decimal  of  a  millimeter  which  the  end  of  the  screw 
moves  for  1  minute  on  the  scale,  gives  the  increase  in 
length  of  the  rod  when  heated  from  0  to  100°.  Again  at- 
tach the  glass  vessel  V,  run  in  ice-water,  cool  the  rod  to 
0,  and  ascertain  the  number  of  minutes  on  the  scale  which 
the  pointer  must  be  turned  to  get  contact  again.  These 
numbers  should  be  very  nearly  the  same.  Average  them, 
and  calculate  the  coefficient  of  linear  expansion  of  the  rod 
for  one  degree,  taking  for  the  length  of  the  rod  the  dis- 
tance between  the  outer  ends  of  the  jacket  corks.  Ar- 
range results  as  follows  : 

Eeading  pointer  at  0      =  min. 

"  "       "  100  =  " 

Pointer  moved  " 

Beading  pointer  at  100  =  " 

tf  ((  (S     A  (f 

Pointer  moved  in  cooling  " 

Average  — 

CALCULATION.  —  Call  the  length  of  the  rod  L,  the  num- 
ber of  minutes  that  the  pointer  moved  m,  and  the  distance 
screw  moved  for  1  m.,  a. 

Then  the  increase  for  100°  =  m  X  a, 
and  the  coefficient  for  100°  =  —  j.  —  , 


and  the  coefficient  for  1°     =         - 

_z/ 

100 


6WBICAL  COEFFICIENT  0#  A  LIQUID.         145 
EXERCISE  10. 

CUBICAL  COEFFICIENT  OF  A  LIQUID. 

EXPERIMENT. 

Apparatus. — Alcohol  of  known  specific  gravity  ;  test-tube  with 
perforated  cork,  and  glass  tube,  with  scale;  tin  pail;  ice-water; 
ring-stand  ;  lamp  ;  thermometer. 

OBJECT. — To  determine  the  cubical  coefficient  of  expan- 
sion of  alcohol. 

MANIPULATION. — Put  some  ice  and  water  in  the  tin  pail, 
and  while  the  mixture  is  cooling  weigh  the  test-tube  with 
the  cork  and  small  tube.  Fill  the  test-tube  nearly  full  of 
alcohol  and  crowd  the  stopper  in  tight,  thus  forcing  a  col- 
umn of  alcohol  up  the  small  tube.  This  column  should 
not  be  over  4  or  5  cm.  high,  and  no  air-bubbles  should  re- 
main in  the  test-tube.  Weigh  again.  The  increase  in 
weight  represents  the  weight  of  alcohol  in  the  apparatus. 
The  volume  is  found  by  dividing  this  weight  by  the  specific 
gravity  of  the  alcohol  (marked  on  the  bottle  from  which  it 
was  taken).  Immerse  the  test-tube  iu  the  ice-water,  allow 
it  to  remain  there  until  the  alcohol  column  has  come  to 
rest,  and  note  the  position  of  the  top  of  the  column  on  the 
scale.  Remove  the  ice  and  slowly  heat  the  contents  of  the 
pail,  stirring  gently  with  the  thermometer  until  the  alcohol 
column  has  risen  four  or  five  cm.  Stop  heating,  and  note 
when  the  alcohol  column  ceases  to  rise.  Read  its  position 
on  the  scale,  and  at  the  same  time  note  the  temperature 
of  the  water.  You  have  now  the  distance  which  the  al- 
cohol rose  in  the  tube  when  heated  from  0  to  the  final  tem- 
perature of  the  water  in  the  pail. 

CALCULATION. — To  determine  the  increase  in  volume, 
multiply  the  rise  on  the  scale  by  the  volume  corresponding 
to  a  rise  of  1  cm.  as  given  on  the  card  attached  to  the  in- 
strument. This  gives  the  increase  in  volume.  Record  re- 
sults as  follows : 


146 

Weight  of  apparatus  +  alcohol      = 
"        empty  = 

"        "  alcohol  =~~ 

.  Volume  of  alcohol  = 

Alcohol  column  read  at  0  = 

(t  ff  ((          f(     4-  __ 

No.  of  degrees  alcohol  was  heated  = 
From  the  data,  calculate  the  cubical  coefficient  of  alcohol 
for  1°. 

EXERCISE  11. 

COEFFICIENT  OF  EXPANSION  OF  A  GAS  AT  CONSTANT  PRESSURE. 

EXPERIMENT  1. 

Apparatus, — The  special  form  in  Fig.  79  ;  ice  or  snow-water  ;  tin 
pail  ;  ring-stand  ;  thermometer  ;  meter-stick.  If  apparatus  is  not 
calibrated  there  will  be  required  in  addition  :  scales  and  weights  ; 
mercury  ;  small  vessel  for  weighing  mercury  ;  burette  or  balances 
that  can  weigh  300  to  400  grams. 

OBJECT. — To  determine  the  coefficient  of  a  gas  under 
constant  pressure. 

MANIPULATION". — To  find  the  volume  of  the  gas  used. 
Having  no  water  in  B,  Fig.  79,  remove  the  gas-holder  A, 
and  by  means  of  a  burette  determine  its  volume  in  cu.  cm.* 
Dry,  and  place  inside  B,  as  shown,  and  connect  with  the 
tube  DC  when  full.  The  volume  of  gas  under  test  is 
really  that  in  A  plus  a  little  in  the  tube  ;  but  since  the  cork 
occupies  some  room  in  A,  it  will  be  near  enough  to  the 
truth  to  call  the  volume  that  of  A  alone.  Fill  B  with 
water  to  about  3  in.  above  the  level  of  A  ;  add  some  ice  or 
snow.  In  a  short  time  the  temperature  of  the  liquid 
should  be  0°.  While  it  is  cooling,  find  the  volume  repre- 
sented by  1  cm.  on  the  tube  DC.  Detach  the  tube  at  E, 
and  draw  a  column  of  mercury  into  it.  Lay  the  tube  on  a 

*  Or,  weigh  A  empty  and  then  full  of  water.  From  the  weight  of 
water  contained  in  A,  calculate  the  volume. 


COEFFICIENT  OF  EXPANSION  OF  A   GAS.       147 


scale  and  measure  the  length  of  the  column.  Call  this 
length  L.  Weigh  a  small  dish;  pour  into  it  the  mercury 
from  the  tube  ;  weigh  the  whole,  and  compute  the  weight 
of  the  mercury  alone.  Call  this  weight  W. 
Then  if  J*  =  specific  gravity  of  mercury,  f 
the  number  of  cu.  cm.  contained  in  length 

W 
L  is  -p  and  the  volume  in  the  tube,  per 

W 

cm.  of  length,  —  -ry .      Put  this  down,  B  ir|i=E:jl- 

labelled  "Volume  per  cm.  in  tube."  It 
is  best  to  repeat  this  several  times  and 
use  the  average  values  obtained. 


FIG.  79. 

Next,  draw  a  small  globule  of  mercury  about  1  cm.  long]; 
into  the  tube,  and  get  it  near  E  by  gently  inclining  the 
tube  and  keeping  the  finger  over  one  end.  This  is  used  as 
an  index.  Attach  the  tube  at  E,  and  read  the  position  of 
the  inner  end  of  the  index  on  the  scale  F.  Before  reading 
it  is  advisable  to  tap  gently  with  a  pencil  on  the  tube  over 
the  index,  as  the  index  is  liable  to  catch  a  little.  If  now 
the  water  in  B  is  at  0°,  add  a  little  warm  water  to  it,  and 
stir  thoroughly  with  the  thermometer  until  a  rise  of  one  or 
two  degrees  in  temperature  takes  place.  As  the  gas  in  4 
increases  in  bulk  the  index  will  move  out  on  the  scale. 
When  the  index  has  assumed  a  constant  position  after  tap- 
ping, and  the  thermometer  is  also  constant  (at  t°),  the  dis- 


*  This  sign  is  called  delta. 
f  Say  13.6. 

\  The  tube  must  be  dry,  and  also  the  mercury, 
end  of  the  meniscus, 


Read  from  the 


148 


HEAT. 


tance  moved  by  the  index  represents  the  increase  in  volume 
A  of  a  cu.  cm.  of  gas  heated  from  0°  to  t°.  From  these  data 
calculate  what  decimal  of  its  bulk  at  0  a  gas  increases  per 
degree  centigrade.  Put  this  down,  carried  out  to  the 
fourth  decimal  place,  and  label  it  "  Coefficient  of  Expan- 
sion." Add  ice  to  J9,  and  repeat  experiment  several  times 
with  different  temperatures  (t°).  Kecord  results  as  follows : 

Volume  of  gas  taken  = 
Vessel  weighed 

TABLE  I. 


Trial. 

Length  Mercury  Col. 

Wt.  Mercury  Col. 

Vol. 

Vol.  per  Cm. 

Average  volume  per  cm.  = 

TABLE  II. 


Index  read 
atO. 

Index  read 
at<° 

Distance 
moved  by 
Index. 

Volume 
corresponding 

Coefficient  of 
Exp.  for  1°. 

Average  value  of  coefficient  = 

A  Second  Method.  The  apparatus  is  shown  in  Fig.  80. 
The  tube  &  is  closed  at  one  end,  and  contains  a  drop  of 
mercury,  g,  to  serve  as  an  index.  The  air  whose  expansion 
is  to  be  measured  is  contained  between  the  closed  end  of 
the  tube  and  the  index.  This  tube  passes  through  a  cork 
in  one  end  of  a  larger  tube,  aa,  which  is  provided  with  an 
inlet  tube  T,  and  an  outlet  tube  T.  The  gas  can  be 
cooled  to  0°  by  filling  the  large  tube  with  ice- water,  and 


EXPANSION  OF  A   GAS  AT  CONSTANT  PRESSURE.  149 

heated  to  100°  by  running  in  steam.  By  measuring  the 
movements  of  the  index,  the  coefficient  may  be  calculated, 
as  in  the  preceding  experiment. 


— \Jc 


11 


FIG.  80. 

EXPERIMENT  2. 

Apparatus.— Special  form  as  shown  in  Fig.  80.  Flask  and  con- 
nections; ring-stand;  gauze  and  burner;  ice- or  snow-water;  funnel, 
and  vessel  to  hold  ice-water;  meter-stick. 

OBJECT. — To  determine  the  cubical  coefficient  of  expan- 
sion of  a  gas  at  a  constant  pressure. 

MANIPULATION. — Run  steam  into  the  large  tube  act. 
As  the  index  is  forced  out,  push  the  tube  in,  keeping  the 
inner  end  of  the  index  just  inside  the  outer  edge  of  the 
cork.  When  the  index  remains  stationary  after  tapping 
with  a  pencil,  measure  the  distance  from  the  inner  end  of 
the  index  to  the  outer  end  of  the  tube.  Disconnect  the 
stearn,  allow  the  apparatus  to  cool  for  a  moment,  and  then 
connect  the  large  tube  with  a  funnel,  and  run  ice-water 
through  until  the  index  again  comes  to  rest,  when  kept 
just  outside  of  the  cork  as  above.  After  tapping  again, 
measure  the  distance  from  inner  end  of  the  index  to  the 
outer  end  of  the  tube.  Eemove  the  tube  and  measure  the 
distance  from  its  open  end  to  the  inner  side  of  the  closet 
end.  Record  results  as  follows: 

Dist.  index  from  end  of  tube  at  100°  = 

te          (t          tf        t(         a        (t        <i        r\o   


Index  moved 
Length  of  tube 


150  HEAT, 

The  length  of  the  tube  minus  the  distance  of  the  index 
at  0  from  the  open  end  gives  the  length  of  air-column 
used. 

CALCULATION. — The  length  of  the  air-column  at  0°  rep- 
resents the  volume  used,  and  the  distance  the  index  moved 
represents  the  increase  for  100°;  so 

r,    ^  .  Increase 

Coefficient  = 


Vol.  at  0°  X  100 
EXERCISE  12. 

ABSORPTION  AND  RADIATION. 

Preliminary. — We  know  that  when  a  heated  body  loses 
heat  by  radiation,  bodies  near  it  are  warmed.  In  the  fol- 
lowing exercise  we  wish  to  study  some  of  the  conditions 
affecting  the  rate  at  which  heat  is  absorbed  by  bodies  when 
exposed  to  radiation.  Under  what  conditions  must  tests 
be  conducted  ?  What  conditions  might  affect  the  amount 
of  heat  absorbed  by  a  body  ? 

In  the  exercise  we  will  use  an  iron  ball  to  radiate  heat, 
and  keep  it  hot  with  a  flame.  To  absorb  the  heat,  we  will 
use  tin  cans  containing  water.  The  cans  are  of  the  same 
size,  but  differ  in  character  of  surface— as  rough  or  bright, 
in  color,  etc.  The  ball  is  suspended  over  the  flame  and 
the  cans  supported  on  blocks,  as  shown  in  Fig.  81. 

*  EXPERIMENT. 

Apparatus.— Part  I :  Ring-stand;  iron  ball  and  wire;  two  flat  tin 
cans  of  the  same  size,  one  covered  with  lamp-black,  each  with  a 
hole  in  the  cover;  blocks  of  wood  to  support  the  cans;  two  thermom- 
eters; watch  or  clock;  water. 

Part  II :    In  addition  to  the  above,  tin  pail  for  heating  some  water. 

OBJECT. — To  investigate  the  effect  of  color,  character  of 
surface,  etc.,  on  the  amount  of  heat  absorbed  or  radiated 
by  a  body. 


AP80RPTION  AND  RADIATION. 


151 


MANIPULATION. — Part  I.  Suspend  the  ball  by  means 
of  a  wire  about  four  inches  above  the  Bunsen  burner  and 
light  the  burner.  Fill  each  can  two-thirds  full  of  water, 
put  on  the  covers,  insert  the  thermometers  through  the 
holes,  and  support  the  cans  at  equal  distances  from  the 
ball  and  on  opposite  sides,  as  in 
Fig.  81.  Read  the  thermometers 
at  intervals  of  a  minute  for  four 
or  five  minutes.  The  cans  are 
best  placed  with  their  largest  flat 
sides  towards  the  ball,  and  great 
care  must  be  taken  that  the  flame 
is  equidistant  between  the  two. 
Avoid  any  draught. 

Part  II.  Fill  both  cans  with 
equal  amounts  of  water  at  about 
10°  above  the  temperature  of  the 
room.  Read  the  thermometers 
again  at  intervals  of  a  minute. 
Tabulate  the  results,  and  state 
what  you  have  learned,  as  regards  FIG.  si. 

the  effect  of  surface,  color,  etc.,  on  absorption  of  heat 
when 

(a)  radiant  heat  strikes  the  surface; 

(b)  the  body  radiates  heat. 

State  in  your  note-book  three  common  examples  of  the 
application  of  these  facts. 

EXERCISE  13. 

SOLUTION. 

EXPERIMENT. 

Apparatus.— Five  test-tubes;  water,  and  means  of  warming  it; 
measuring-cylinder;  scales  and  weights  (if  solids  are  not  ready 
weighed);  powdered  and  lump  sugar;  burner;  sand;  iodine;  copper 
sulphate;  alcohol. 

OBJECT.— To  observe  the  conditions  affecting  solution. 


152  HEAT. 

MANIPULATION. — Part  I.  Take  two  test-tubes,  place  in 
each  0.5  gram  of  powdered  sugar;  to  one  add  5  and  to 
the  other  10  cu.  cm.  of  warm  water.  Cork  the  tubes,  and 
shake  gently  until  all  the  sugar  is  dissolved  ;  then  add  a 
second  0.5  gram  to  each,  and  so  proceed  as  long  as  the  so- 
lution goes  on.  Set  the  tubes  aside.  Can  any  amount  of 
sugar  be  dissolved  in  a  given  amount  of  water  ?  Does  the 
volume  of  water  used  have  any  effect  ? 

Part  II.  Place  a  piece  of  lump-sugar  weighing  about 
0.5  gram  in  one  tube,  and  an  equal  weight  of  powdered 
sugar  in  another.  Put  about  5  cu.  cm.  of  warm  water  in 
each,  shake  gently,  and  observe  the  time  required  to  dis- 
solve. Does  the  condition  of  the  body  make  any  differ- 
ence? 

Part  III.  Warm  one  of  the  tubes  containing  the  solu- 
tions formed  in  Part  I.  Then  add  another  0.5  gram  sugar, 
and  heat.  Does  the  temperature  of  the  water  have  any 
effect  on  its  power  to  dissolve  ? 

Part  IV.  Take  five  test-tubes,  place  in  them  about 
equal  amounts  (0.25  gram)  of  sugar,  sand,  iodine,  copper 
sulphate,  and  alcohol.  Add  to  each  5  cu.  cm.  of  water. 
Are  all  bodies  equally  soluble  ?  Can  one  liquid  dissolve  in 
another  ? 

Part  V.  Repeat  the  experiment  with  alcohol.  Does  the 
nature  of  the  liquid  make  any  difference  ? 

Part  VI.  Place  about  40  cu.  cm.  warm  water  in  a  meas- 
uring-cylinder; read  the  volume;  now  put  into  the  water 
0.5  gram  of  powdered  sugar,  and  again  read  the  vol- 
ume. When  the  sugar  has  dissolved,  read  the  volume 
again.  What  effect  on  the  volume  of  the  liquid  is  pro- 
duced by  dissolving  a  solid  in  it  ? 

Tabulate  all  the  conditions  that  you  have  found  affected 
the  solution. 


DYNAMICS. 


EXERCISE  1. 

ACTION  OF  A  FORCE  UPON  A  BODY. 

Preliminary. — In  the  following  exercise  we  wish  to 
study  the  behavior  of  a  body  when  a  force  acts  upon  it. 
The  force  must  be  applied  to  a 
body  that  is  free  to  move,  or  we 
cannot  be  sure  that  anything  ob- 
served is  due  to  the  action  of  the 
force  alone.  If  the  body  is  sus- 
pended, the  suspending  wire  takes 
its  weight,  and  there  is  nothing  to 
prevent  its  responding  freely  to 
forces  applied  horizontally.  A 
string  may  be  attached  to  the  body, 
and  pulled  in  various  directions  in 
a  horizontal  plane  and  with  differ- 
ent degrees  of  force.  The  degree 

of  force  may  be  approximately,  but  not  accurately,  meas- 
ured by  attaching  a  spring-balance. 

EXPERIMENT  1. 

Apparatus.— Heavy  body  suspended  by  a  wire  ;  piece  of  cotton 
string  ;  two  spring-balances  for  Experiments  2  and  3. 

OBJECT. — To  see  (1)  what  happens  when  a  force  acts  on 
a  body,  and  (2)  the  effect  of  the  direction  of  the  action. 

MANIPULATION. — Arranging  the  apparatus  as  shown 
in  Fig.  82,  pull  the  string  from  various  points  of  com- 
pass, always  at  the  height  of  the  ball  and  parallel  with  the 

153 


154 


DYNAMICS. 


table.    Make  five  trials,  and  record  the  results  in  a  table 
arranged  as  follows: 


TABLE  I. 


Direction 
of  Pull. 

Action  of  Body. 

Indicate  the  direction  of  the  pull,  by  inserting  N.  for 
north  ;  W.  for  west ;  N.E.  for  north-east;  etc. 

EXPERIMENT    2. 

OBJECT. — To  see  the  effect  produced  by  the  magnitude 
of  the  force. 

MANIPULATION*. — Attach  a  spring-balance  to  the  string. 
Pull  suddenly  on  the  balance,  trying  to  vary  the  amount 
of  the  pull  without  altering  the  time  during  which  it  is 
applied.  A  sudden  "yank"  is  best,  only  not  hard 
enough  to  break  the  string.  Observe  approximately  the 
amount  of  the  body's  motion  and  the  strength  of  the  pull 
as  shown  by  the  reading  of  the  balance-index.  Only  gen- 
eral results  are  expected.  Make  four  trials,  and  record  the 
results  as  follows*: 

TABLE  II. 


Force. 

Motion. 

Direction. 

- 

In  columns  1  and  2  insert  the  words,  "more,"  "less,"  or 
"same,"  as  the  case  maybe.  In  the  third  column  place 
the  initials  of  the  points  of  compass,  as  before. 


ACTION  OF  A  FORCE  UPON  A  BODY. 


155 


QUESTIONS. — What  is  the  inference  in  regard  to  the 
magnitude  of  the  force  ?  Does  the  direction  in  which  the 
force  acts  make  any  difference  in  this  respect  ?  Make 
several  trials  in  each  direction,  say  three,  making  twelve 
trials  in  all.  By  studying  the  data  obtained  in  both  these 
experiments  make  a  summary  of  what  is  indicated,  as  re- 
gards the  action  of  a  force  on  a  body,  in  relation  to  (1) 
motion  of  the  body,  (2)  direction  of  the  motion  as  com- 
pared to  the  direction  of  the  force,  (3)  amount  of  the 
motion  as  compared  to  the  amount  of  the  force.  [This  last 
in  general  terms  only.*] 

EXPERIMENT  3. 

OBJECT. — To  observe  the  effects  of  equal  and  unequal 
forces  acting  in  opposite  directions. 

MANIPULATION. — Attach  two  spring-balances  by  strings 
to  the  weight  and  pull  in  opposite  directions.  Observe 
the  motion  of  the  body  when  the  forces  are  equal.  By 
suddenly  pulling  stronger  on  one  balance,  render  them  un- 
equal, and  observe  the  results.  Try  several  times,  apply- 
ing the  two  forces  in  various  directions,  but  always  opposite 
to  each  other  and  parallel  to  the  table.  Mark  one  force  -}- 
and  one  —  and  record,  in  a  table,  as  follows : 

TABLE  III.  » 


+  Force. 

—  Force. 

Result  on  Body. 

Under  each  force  place  its  value,  obtained  by  reading 
the  balance,  and  in  the  third  column  insert  the  words, 
"  moved"  or  "  no  motion,"  as  the  case  may  be.  In  case 
the  body  moved  in  the  direction  of  the  -j-  force,  place  the 


156  DYNAMICS. 

-j-  sign  before  the  word  "  moved  " ;  if  in  the  opposite  direc- 
tion, the  —  sign. 

QUESTIONS. — 1.  Under  what  conditions  does  the  body 
move  ?  Under  what  conditions  does  it  remain  at  rest  ?  2. 
Does  the  fact  that  a  body  is  acted  on  by  forces  necessarily 
mean  that  the  body  will  move  ?  When  a  body  is  acted  on 
by  forces  and  the  opposite  forces  are  equal,  it  is  said  to  be 
in  equilibrium.  Place  in  the  note-books  two  cases  of 
equilibrium  that  you  know  of,  and  explain  in  each  case 
how  the  equilibrium  is  obtained. 

EXERCISE  2. 

THE  FORCE  OF  FRICTION. 

Preliminary. — "When  two  surfaces  are  rubbed  together 
some  force  is  exerted.  This  fact  is  said  to  be  due  to  fric- 
tion of  the  surfaces,  and  the  force  with  which  the  surfaces 
resist  being  rubbed  is  said  to  be  due  to  the  force  of  friction. 
In  the  following  exercise  we  wish  to  study  the  conditions 
which  affect  the  magnitude  of  this  force.  We  must  meas- 
ure the  force  under  various  conditions.  Since  the  force 
required  to  keep  a  body  moving  over  a  level  surface  is 
equal  to  the  force  of  friction  acting  upon  it,  if  we  ascertain 
the  magnitude  of  one  force,  we  know  that  of  the  other. 
By  turning  the  block  used  in  the  experiments  edgeways  or 
flat,  we  can  vary  the  extent  of  surface  rubbed ;  and  by  lay- 
ing one  or  two  blocks  on  the  first,  we  can  double  or  treble 
the  weight  without  altering  the  extent  of  surface. 

EXPERIMENT. 

Apparatus.— Board;  blocks  of  wood;  8-oz.  balance  or  rubber-strip; 
string. 

OBJECT. — To  study  the  conditions  affecting  the  magni- 
tude of  the  force  of  friction. 

MANIPULATION.— Lay  the  block  of  wood  on  its  smooth, 


THE  FORCE  OF  FRICTION. 


157 


flat  side,  and  draw  it  along  the  board  at  a  uniform  rate  of 
speed.  Two  students  should  work  together  on  this  experi- 
ment. One  student,  holding  the  balance  horizontally  on 
the  palm  of  one  hand,  and  grasping  its  ring  with  the  other 
hand,  should  devote  his  whole  attention  to  reading  the  bal- 
ance as  his  hands  slide  along  the  board,  with  a  view  to  de- 
termining the  average  position  of  the  pointer.  The  other 
student  should  see  that  the  motion  is  uniform  and  the 
pull  parallel.  Repeat  several  times,  recording  the  force 
observed  each  time.  ^  Repeat  with  the  block  turned  on 
edge.  Lay  the  block  flat  and  place  a  second  one  on  it. 
Measure  the  force  again.  Try  again  with  two  blocks  laid 
on  the  first.  Repeat  the  first  part  with  the  rough  side  of 
the  block  down.  Tabulate  results  as  follows: 


Position  of  Block. 

Force. 

Av.  Force. 

No.  of  Blocks. 

Trial. 

QUESTIONS.— 1.  What  effect  has  the  extent  of  surface 
on  the  force  of  friction  ?  2.  What  effect  has  the  weight  ? 
3.  What  effect  has  the  character  of  the  surface  ?  4. 
Weigh  one  block  and  calculate  the  coefficient  of  friction 
for  all  the  weights,  taking  two  blocks  as  twice  the  weight 
of  one  block,  etc. 

Measurement  of  Forces.  — If  forces  are  to  be  compared  as 
to  strength,  we  must  have  a  unit  of  force,  just  as  we  had  units 
of  length,  volume,  etc.  We  need  for  this  unit  a  force  that 
can  be  readily  obtained,  and  easily  used  for  purposes  of 
comparison.  The  force  selected  is  gravitation,  as  shown 
in  the  pull  of  the  earth  on  bodies  upon  its  surface.  1'his 
pull  has  been  found  to  be  always  the  same  for  the  same 
body  at  the  same  place,  but  in  order  to  get  a  definite  pull 


158  DYNAMICS. 

we  must  also  specify  the  quantity  of  matter  to  be  pulled. 
The  unit  of  force  is  taken  as  the  pull  of  the  earth  on  a  unit 
weight — say  a  pound  weight  or  a  gram  weight;  thus  a  force 
of  one  pound  would  be  a  push  or  pull  equal  to  the  pull  of 
the  earth  on  a  pound  weight.  In  order  to  pull  with  a 
force  of  one  pound,  you  would  have  to  exert  your  muscles 
as  much  as  in  holding  a  pound  weight.  In  the  same  way, 
a  force  of  one  gram  would  be  a  force  equal  to  the  pull  of 
the  earth  on  a  gram  weight. 

PROBLEMS. — Explain  what  is  meant  by:  1.  A  force  of  6 
Ibs.?  2.  A  force  of  1  ounce?  3.  A  force  of  10  grams? 
4.  A  force  of  1  ton?  5.  A  force  of  6  kilograms?  A 
pound  weight  weighs  453  grams.  A  force  of  2  Ibs.  would 
be  the  force  of  how  many  grams  ? 

There  are  two  ways  of  measuring  forces — by  weights  and 
by  a  spring-balance.  In  the  first  way,  the  weights  are 
made  to  pull  against  the  force  to  be  measured,  and  a  suf- 
ficient number  of  weights  are  used  to  just  balance  the 
force.  The  sum  of  the  weights  shows  the  value  of  the 
force.  In  the  second  way,  the  force  to  be  measured  is 
made  to  stretch  the  spring  of  the  balance,  and  the  value  of 
the  force  is  given  by  the  index.  A  spring-balance  when 
used  for  measuring  force  is  sometimes  called  a  Dynamom- 
eter. 

Graphical  Representation  of  Forces. — To  represent  a 
force  whose  magnitude,  direction,  and  point  of  application 
are  known,  we  proceed  as  follows: 

1.  Make  a  point  for  the  point  of  application. 

2.  To  that  point  rule  a  straight  line  whose  direction  is 
the  direction  of  the  force. 

3.  Assuming  some  particular  length  to  represent  a  unit 
of  force,  with  compasses  or  scale  lay  off  this  length  along 
the  line  of  direction  as  many  times  as  there  are  units  of 
force. 

For  example,  suppose  we  have  to  represent  a  force  of  6 


FORCE!  OF 


159 


Ibs.  magnitude  acting  in  an  upward  direction  on  the  line 

ab,  Fig.  83.     Mark  the  point  of  ap-  a    c e      b 

plication  anywhere  on  the  line,  say 
at  c.  To  c  draw  a  straight  line  cd. 
Starting  at  c,  with  a  scale  of  1  cm.  to 
1  lb.,  lay  off  along  cd  a  distance  of 
6  cm.  Suppose,  again,  we  wish  to 
represent  another  force  of  3  Ibs.  act- 
ing at  e.  Draw  to  e  a  line  eg,  and 
from  e  lay  off  on  it  3  cm.  The  di- 
rection of  a  force  is  sometimes  rep- 
resented by  an  arrow.  The  fact 
that  forces  are  acting  in  opposite 
directions  is  also  indicated  by  giv- 
ing one  the  -f-  sign  and  the  other  the  FlG-  83« 

—  sign.     Commonly,  -f  is  used  for  the  upward  direction 
and  —  for  the  downward,  +  toward  the  right  and  —  to- 
ward the  left,  but  since  the  general  rule  is  to  mark  one 
force  -f-  and  all  forces  whose  general  direction  is  opposite 
— ,  the  direction  -f-  represents  should  be  stated  in  each 
diagram.     Forces  are  added  by  laying  off  on  the  line  rep- 
resenting the  forces  of   one  sign  a  line  representing  the 
forces  of  opposite  sign.     Thus,  to  find  by  construction  the 
sum  of  +  6  and  —  4,  lay  off  on  the  line  -f-  6  a  distance 
equal  to  —  4.     The  part  of  the  length  not  used  up  by  the 

—  length  is  the  required  sum,  -f-  2  in  this  case. 

A  problem  can  be  worked  out,  as  most  convenient,  by 
geometry,  using  lines  as  above,  or  by  algebra,  using  num- 
bers and  signs.  In  the  latter  method  the  sign  prefixed  to 
the  magnitude  of  a  force  indicates  its  direction  relative  to- 
the  other  forces.  These  magnitudes  are  added  and  sub- 
tracted as  other  algebraic  quantities.  Thus  the  sum  of 
two  faces,  one  -j-  6  and  —  4  is  a  force  of  -j-  2. 


160  DYNAMICS. 

EXERCISE  3. 

COMPOSITION  OF  FORCES. 

Preliminary. — A  force  that  in  its  action  on  a  body  is 
equal  to  the  combined  effects  of  several  forces  is  called  the 
resultant  of  those  forces.  For  example,  a  single  force 
which  will  produce  the  same  effect  on  a  horse-car  as  the 
force  exerted  by  the  two  horses  would  be  the  resultant  of 
the  forces  exerted  by  the  horses.  The  process  of  finding 
the  resultant  of  several  forces  is  called  the  composition  of 
forces.  The  reverse  process,  finding  several  forces  whose 
combined  effect  on  a  body  is  equal  to  that  of  a  given  force, 
is  called  resolving  that  force,  and  the  equivalent  forces 
found  are  called  its  components. 

We  can  apply  more  than  one  force  to  a  body  at  one 
point  in  two  ways. 

(a)  We  can  apply  the  forces  in  one  straight  line,  in  the 
same  direction  or  in  opposite  directions,  as  a  number  of 
engines  drawing  a  train,  or  two  men  pulling  against  each 
other  OR  a  rope.     In  the  first  case  each  force  adds  its  effect 
to  that  of  the  others;  in  the  second  case,  the  lesser  force 
diminishes  the  effect  of  the  greater.     The  resultant  of  the 
forces  in  each  case  is  their  algebraic  sum.     For  example,  a 
wagon  is  pulled  by  three  horses  tandem,  each  exerting  a 
force  of  1000  Ibs. ;  the  same  effect  on  the  wagon  would  be 
caused  by  one  horse  exerting  a  force  of  3000  Ibs.     Or,  again, 
a  body  is  acted  upon  by  two  opposite  forces,  -f-  8  —  3,  in 
strength;  the  same  effect  would  be  produced  on  the  body 
by  a  single  force  -|-  5  in  strength. 

(b)  We  can  apply  the  forces  at  an  angle  to  each  other. 
Suppose  two  forces  act  on  the  same  point,  one  pulling  it 
east  and  one  pulling  it  north.     Can  a  single  force  be  found 


COMPOSITION  OF  FORCES. 


161 


that,  when  applied  alone  to  the  point,  will  produce  the  same 
effect  as  the  two  forces?  To  answer  this  question  we  must 
let  two  forces  act  on  a  body  at  an  angle,  and  see  if  we  can  sub- 
stitute for  them  one  force  that  will  produce  the  same  effect. 
If  we  can  do  so,  the  substituted  force  will  be  the  resultant. 
Two  balances,  A  and  B,  Fig.  84,  are  joined  by  a  cord. 
On  this  cord  slides  another  whose  ends  are  attached  to  two 


Fi«.  84. 

other  balances,  C  and  D.  A  and  B  are  fastened  to  the 
table,  and  by  pulling  on  (7  two  forces  will  act  on  the  point 
a  at  an  angle  AaB.  The  balance  C  will  hold  this  point 
against  the  combined  action  of  A  and  B,  and  this  com- 
bined action  will  pull  the  index  of  C  down  to  a  certain 
point,  and  a  will  take  a  certain  position  which  can  be 
marked.  Now  if  we  release  A  and  B,  and  by  pulling  on  D, 
as  in  Fig.  85,  can  bring  a  to  the  same  point,  we  shall  have 
substituted  the  pull  of  a  single  balance  for  the  combined 
pulls  of  the  two  balances,  A  and  B.  It  will  be  also  desir- 
able to  find  out  whether  a  single  force  acting  on  a  point  can 
be  resolved  into  two  components  acting  at  an  angle  on  the 
same  point.  We  can  do  this  by  pulling  on  a  with  a  certain 
force  registered  on  C,  and  then  trying  to  substitute  angu- 
lar pulls  by  A  and  B  that  will  bring  a  to  the  same  point. 


162 


DYNAMICS. 


EXPERIMENT   1. 

Apparatus.— Four  24-lb.  balances;  fish-line;  scale;  dividers;  nails; 
wooden  block. 

OBJECT. — When  two  forces  act  at  an  angle  on  the  same 
point,  to  find  one  force  whose  effect  on  the  point  is  the 
same  as  the  combined  effects  of  the  other  two. 

MANIPULATION. — Arrange  apparatus  as  in  Fig.  84,  A  and 
B  being  fastened  to  the  table.  Pull  on  C  in  any  direction 
until  it  and  A  and  B  read  over  five  pounds.  In  a  general 
way,  the  stronger  the  pulls  the  better,  only  care  must  be 
used  not  to  break  the  strings.  Either  hold  the  balance  C 
steady;  or,  better,  secure  it  by  a  nail  passing  through  the 
ring  and  driven  into  the  table.  Read  the  balances,  and 
mark  the  position  of  the  point  a  on  the  table.  Pull  on  D 
with  a  force  of  a  few  pounds,  and,  still  keeping  a  strain  on 
D,  gently  release  the  balances  A  and  B.  Then  by  pulling 
on  D,  find  the  direction  and  magnitude  of  a  force  that  will 
bring  a  to  exactly  the  same  point  as  when  acted  on  by  A 
and  B.  If  you  succeed  in  doing  this,  you  will  have  one 
force  producing  the  same  effect  on  a  as  the  combined  forces 
A  and  B.  Make  several  trials,  and  record  the  results  as 
follows: 


Force  A. 

Force  B. 

Force  C. 

Force  D. 

QUESTIONS. — 1.  How  do  C  and  D  compare  in  magni- 
tude? 2.  How  do  they  compare  in  direction?  3.  How 
does  the  general  direction  of  D  compare  with  that  of  A  and 
B?  4.  How  does  the  magnitude  of  D  compare  with  those 
of  A  and  of  B?  5.  How  does  the  magnitude  of  D  com- 
pare with  the  sum  of  the  magnitudes  of  A  and  C? 


COMPOSITION  OF  FORGES.  163 

EXPERIMENT  2. 

Apparatus.— Four  spring-balances;  stout  string;  nails:  etc. 

OBJECT. — To  find  two  forces  that,  if  applied  to  one  point 
at  an  angle  to  each  other,  will  produce  the  same  effect  as  a 
single  given  force  applied  to  the  same  point. 

MANIPULATION. — Arrange  apparatus  as  in  Fig.  85,  A 
and  B  being  loose  and  C  being  fastened  to  the  table.  Pull 
on  D  with  any  desired  force  in  any  direction,  and  note  the 
readings  of  C  and  D  and  the  position  of  a.  Substitute  for 


FIG.  85. 

D,  A  and  B  pulled  at  an  angle.  See  if  their  combined 
effect  can  be  made  to  bring  a  to  the  point  where  it  was 
when  C  and  D  alone  acted  on  it.  Make  several  trials  with 
a  view  to  finding  out  whether  more  than  one  combination 
of  A  and  B  can  take  the  place  of  D.  Eecord  in  each  case 
the  balance  readings,  and  the  angles  made  by  A  and  B  as 
estimated  by  the  eye. 

QUESTIONS. — 1.  Can  two  forces  produce  the  same  effect 
as  one  ?  2.  Can  they  be  substituted  for  one  ?  3.  How 
do  their  magnitudes  compare  with  that  of  the  one  for 
which  they  are  substituted  ?  4.  .Can  more  than  one  set  of 
forces  be  substituted  for  the  given  force  ? 

Parallelogram  of  Forces. — The  next  thing  is  to  find  a 
way  to  express  graphically  the  relation  of  the  resultant 
and  its  components.  The  readings  of  A  and  B  in  the 


164  DYNAMICS. 

apparatus  represented  in  Fig.  84  will  give  the  magnitudes, 
and  the  strings  the  directions  of  the  components.  Taking 
these  directly  from  the  apparatus,  we  can  construct  a 
parallelogram  whose  two  adjacent  sides  represent  the  two 
components.  Since,  as  we  have  just  seen,  the  third  force, 
(7,  is  equal  and  opposite  to  the  resultant,  we  can  include 
the  resultant  in  the  parallelogram  by  taking  the  reading 
of  C  for  its  magnitude  and  making  its  direction  exactly 
opposite  to  that  of  the  string  Ca.  In  the  diagram  we  can 
look  for  any  geometrical  relation  that  may  exist  between 
component  and  resultant  forces. 

EXPERIMENT  3. 

Apparatus.—  Same  as  in  Exp.  2,  and  a  thick  block  of  wood  to  be 
used  as  a  ruler. 

OBJECT. — When  two  forces  act  at  an  angle  on  the  same 
point,  to  express  graphically  the  relation  between  them 
and  their  resultant. 

MANIPULATION. — Proceed  as  in  Exp.  2.  When  all  three 
balances  are  pulling  on  the  point  a,  place  the  note-book 
under  the  strings  so  that  the  knot  comes  about  in  the 
centre  of  the  page,  Fig.  84.  Bring  the  block  of  wood 
gently  up  to  one  of  the  strings  so  as  to  just  touch  it  at  all 
points,  and,  using  it  as  a  ruler,  draw  a  line  a  few  inches 
long.  This  line  should  represent  exactly  the  direction  of 
the  string.  Great  care  must  be  used  not  to  move  the 
string  and  not  to  let  the  block  of  wood  touch  the  knots  at 
either  end.  The  harder  the  balances  are  pulling,  the  less 
the  string  is  likely  to  be  deflected.  Do  the  same  with  the 
other  two  strings,  using  great  care  that  the  note-book  does 
not  change  its  position  during  the  operation.  Read  each 
balance,  and  put  its  reading  at  the  outer  end  of  the  corre- 
sponding line.  Remove  the  note-book,  and  by  means  of  a 
ruler  prolong  the  lines  until  they  meet  at  a  point  as  indi- 
cated by  the  dotted  lines  in  Fig.  86.  This  is  the  point,  a, 


COMPOSITION-  OP  FORCES.  165 

which  was  directly  under  the  knot.  You  have  now  the 
magnitude,  direction,  and  point  of  application  of  the  three 
forces.*  Starting  from  the  point  a,  lay  off  on  the  lines 


FIG.  86. 

9  and  8  the  magnitudes  corresponding,  representing  \  Ib. 
hy  the  largest  unit  of  length  the  note-book  page  permits. 
Construct  a  parallelogram,  of  which  the  point  a  forms  one 
angle  and  the  lines  representing  the  two  forces  9  and  8 
form  the  sides  adjacent.  The  junction  of  the  opposite 
sides  is  found  by  prolonging  the  line  representing  the 
third  force,  12,  as  a  diagonal  through  this  parallelogram, 
and  from  a  laying  off  on  it  a  distance  equal  to  that  force. 
Make  as  many  trials  as  time  allows,  using  various  forces. 
From  the  study  of  the  diagrams  so  obtained  make  a  rule 
for  finding,  by  means  of  a  diagram. 

1.  The  resultant  of  two  forces  whose  magnitudes  and 
directions  are  known. 

2.  The  components  of  a  given  force. 

*  Before  laying  off  the  forces,  the  balance-readings  should  be 
corrected  for  position  error  and  zero  error,  if  these  errors  are  of 
magnitude.  Usually,  however,  as  they  tend  to  counteract  each 
other,  the  total  error  is  so  slight  that  it  may  be  neglected.  The 
record  in  the  note-books  should  state  whether  or  not  corrected 
readings  are  used. 


166  DYNAMICS. 


EXERCISE  4. 

PARALLEL  FORCES. 

Preliminary. — So  far  as  we  have  considered  cases  where 
the  forces  had  the  same  point  of  application;  but  there  is 
another  case.  Suppose  the  body  cib,  Fig.  87,  to  be  acted 

on  by  two  parallel  forces,  x  and 
>*  y.  A  good  illustration  of  this  is 

where  a  carriage  is  pulled  by  a 
~^y  span  of  horses.  In  this  case  it 
FIG.  87.  is  evident  that  the  two  forces 

have  different  points  of  application,  and  that  the  resultant 
has  a  still  different  point.  Forces  applied  in  this  way  are 
called  parallel  forces.  To  investigate  the  case  of  parallel 
forces  the  apparatus  shown  in  Fig.  88  is  used.  By  pulling 
dowi  on  the  balances  B  and  (?,  parallel  forces  act  on  the 
meter-stick,  and  the  combined  pull  of  the  two  is  taken  by 
balance  A.  The  readings  of  B  and  C  give  the  magnitudes 
of  the  components,  and  the  reading  of  A  the  magnitude 
of  a  force  which  is  equal  and  opposite  to  the  resultant  (as 
in  Ex.  3),  and  whose  point  of  application  is  the  same  as 
that  of  the  resultant.  With  these  data  we  can  investigate 
the  relations,  as  regards  magnitude,  point  of  application, 
etc.,  of  parallel  components  and  resultant. 

EXPERIMENT  1  . 

Apparatus.— Three  24-lb.  balances;  meter-stick;  fish-line;  means  of 
suspending  meter-stick  (the  whole  arranged  as  in  Fig.  90). 

OBJECT. — When  two  parallel  forces  act  on  a  rigid  body, 
to  determine  (1)  the  relation  of  the  resultant  to  the  com- 
ponents in  magnitude  and  direction;  (2)  the  position  of 
the  point  of  application  of  the  resultant  with  reference  to 
those  of  the  components;  (3)  under  what  conditions  equi- 
librium may  be  obtained;  and  (4)  under  what  conditions 
the  body  tends  to  rotate. 


PARALLEL  FORCES.  167 

MANIPULATION. — The  readings  of  B  and  (7,  Fig.  88, 
when  forces  are  applied  will  not  represent  the  true  forces, 
because  the  balances  themselves  weigh  something,  and  alone 


FIG.  88. 

exert  a  slight  downward  pull.  To  correct  for  this  error, 
detach  the  apparatus  from  the  balance  A,  slip  the  loops  of 
string  off  from  the  meter-stick,  and  weigh  balances  B  and 
G  on  A.  Take  half  the  weight  so  obtained  as  the  weight 
of  one  balance.*  Again,  since  balance  A  has  to  support  the 
weight  of  the  meter-stick  in  addition  to  the  forces  used, 
the  weight  of  the  meter-stick  must  be  found.  Remove 
balances  B  and  G  from  A,  suspend  the  meter-stick  alone, 
and  record  the  reading  of  A.  Since  this  reading  also  gives 
A's  increased  reading  due  to  the  zero,  error,  we  have  the 
total  amount  to  be  subtracted  from  each  subsequent  read- 
ing in  order  to  get  the  true  force  exerted  on  A  by  the  com- 
bined pulla  of  B  and  G.  When  ready  for  work,  the  table 
of  errors  should  stand  something  like  this: 

Correction  for  weight,  B ....  G.  . .  .A . . . . 

"         to  zero,        B....C 

Record  on  which  side  of  the  pointer  the  readings  were 
taken. 

Slide  the  loops  of  the  strings  from  B  and  G  to  such 

*  These  weighings  could  be  still  better  performed  with  a  04-02. 


168 


DYNAMICS. 


points  on  the  stick  that  the  distance  of  each  loop  from  the 
centre  is  over  10  cm.  Pull  down  steadily  on  the  two  lower 
balances,  being  careful  to  pull  vertically,  until  each  balance 
reads  more  than  five  Ibs.  Read  the  three  balances,  and  note 
the  direction  of  balance  A.  Place  the  loops  at  different 
points  on  the  stick,  and  try  again.  Try  a  case  where  the 
distance  on  one  side  is  twice  that  on  the  other.  Try  a  case 
where  the  distances  are  both  alike.  Try  other  cases,  mak- 
ing six  in  all.  Great  care  must  be  used  in  reading  the 
balances  as  accurately  as  possible,  and  always  from  the 
side  of  the  pointer  used  in  getting  the  readings  for  errors. 
Tabulate  the  results  as  follows : 

TABLE  I. 


Read.  A. 

Read.  B. 

Dist.  B. 

Read.  C. 

Dist.  C. 

Direc.  A. 

Trial. 

While  you  have  equilibrium,  increase  the  pull  of  one 
balance.  Note  what  happens.  Decrease,  and  note  again. 

CALCULATION'. — The  balance-readings  have  three  errors 
for  which  corrections  must  be  made:  (1)  Owing  to  use,  tlje 
balances  all  read  high;  (2)  A  reads  high  because  of  the 
weight  of  the  apparatus;  (3)  The  readings  of  B  and  0  show 
the  forces  applied  less  the  weight  of  the  balances  them- 
selves and  their  zero-errors.  Correct  A  by  subtracting  total 
weight-error.  Correct  B  and  0  for  zero-error,  and  add 
their-weight.  Record  the  results  as  follows,  giving  cor- 
rected readings: 

TABLE  II. 


Read.  A. 

Read.  B. 

Read.  C. 

Dist.  B. 

Dist.  C. 

CxDc 

BXDb 

The  values  obtained  by  multiplying  the  magnitudes  of 
parallel  forces  by  their  "  leverage/'  that  is,  the  distance  of 


THE  INCLINED  PLANE.  169 

the  point  of  application  of  each  force  from  the  same  point 
of  reference,  as  G  X  Cd,  Fig.  88,  are  called  the  moments 
of  the  forces. 

QUESTIONS. — 1.  Can  you  see  any  relation  between  A,  B, 
and  O  as  regards  (a)  direction;  (b)  magnitude?  2.  Is 
anything  noticeable  on  comparing  the  moments  of  B  and  C 
for  each  case  ?  3.  Can  you  make  out  any  relation  between 
B  and  Db  that  also  exists  between  C  and  DC  ?  4.  When 
the  stick  is  at  rest,  how  do  the  moments  of  B  and  C  com- 
pare? 5.  When  the  moment  of  one  force  was  made  larger 
than  the  other,  by  suddenly  pulling  down  on  one  balance, 
what  happened  ?  6.  Can  you  name  a  case  in  which  the 
principle  of  this  experiment  is  used  ? 

EXERCISE  5. 

THE  INCLINED  PLANE. 

Preliminary. — We  know  that  machines  enable  us  to 
make  a  small  force  overcome  a  greater  one,  but  do  they 
save  work  ?  When  a  force  is  overcome  by  the  aid  of  a  ma- 
chine, is  any  less  work  done  than  when  the  force  is  over- 
come directly  ?  For  example,  if  a  weight  is  lifted  directly 
10  ft.,  or  lifted  the  same  distance  by  a  machine,  is  the 
work  done  in  the  former  case  any  more  than  that  done  in 
the  latter  ?  To  answer  this  question,  we  may  raise  a  known 
weight  a  known  vertical  distance  by  means  of  a  machine, — 
say  an  inclined  plane, — and  compare  the  work  done  in  this 
case  with  that  done  in  lifting  the  body  vertically  the  same 
distance.  For  this  purpose  the  apparatus  illustrated  in 
Fig.  89  may  be  used.  The  board  B  forms  the  inclined 
plane,  and  may  be  set  at  any  angle  by  adjusting  the  rod  R 
of  the  support  S.  The  weight  to  be  raised  is  the  loaded 
carriage  (7,  and  the  force  required  to  pull  it  up  the  plane 
may  be  obtained  from  the  reading  of  the  balance  B.  We 
can  get  the  work  done  in  raising  the  body  vertically  by 
multiplying  the  total  weight  of  the  body  by  the  distance  it 


170 


DYNAMICS. 


is  raised  (say  db  in  the  figure),  and  the  work  done  in  rais- 
ing it  by  the  plane  by  multiplying  the  force  required  to  pull 


FIG.  89. 

the  body  up  the  plane  by  the  distance  that,  it  must  travel 
on  the  plane,  cb  in  the  figure,  to  reach  the  required  height. 

EXPERIMENT. 

Apparatus.— Board  of  Exercise  2;  support;  weighted  carriage; 
24 -Ib.  balance;  cross-stick  and  cord;  meter-stick;  T-square  or 
plumb-line. 

OBJECT. — 1.  To  study  the  laws  of  the  inclined  plane.  2. 
To  see  if  a  machine,  taking  the  inclined  plane  as  an  exam- 
ple, saves  work. 

MANIPULATION. — Get  the  weight  of  the  carriage  and 
load  together.*  In  case  no  suitable  scales  can  be  had,  the 
weight  may  be  found  with  sufficient  accuracy  by  means  of 
the  spring-balance.  Adjust  the  support  so  that  the  board 
B  is  inclined  at  an  angle  of  about  30  degrees.  Hook  the 
balance  into  the  loop  at  the  end  of  the  cord  connected  with 
the  carriage.  Let  one  student  hold  the  balance  firmly  in 
both  hands,  and  draw  the  carriage  up  the  plane  at  a  uni- 
form rate  of  speed.  The  back  of  one  hand  should  rest  on 
the  board  upon  which  it  slides,  and  his  entire  attention 
should  be  devoted  to  holding  the  balance  firmly,  and  pull- 
ing the  carriage  at  a  uniform  rate.  He  should  pull  exactly 
parallel  to  the  plane,  and  hold  the  balance  so  that  it  will 
not  bind,  keeping  his  eyes  away  from  the  balance  altogether. 

*  This  weight  may  be  determined  once  for  all,  and  marked  upon 
the  carriage. 


THE  INCLINED  PLANE.  171 

Meantime  let  the  second  student  keep  his  eye  directly  over 
the  balance  and.  take  as  many  readings  as  possible.  Owing 
to  little  inequalities  in  the  board,  etc.,  these  readings  will 
vary  slightly,  and  the  average  position  of  the  index  must  be 
determined  as  accurately  as  possible.  A  number  of  trials 
should  be  made,  the  students  alternating  in  reading  the 
balance,  etc.,  and  different  parts  of  the  board  being  used. 
The  average  of  these  trials,  after  the  following  corrections 
have  been  made,  will  give  very  closely  the  force  required  to 
pull  the  carriage  and  load  up  the  plane. 

The  force  used  to  pull  the  body  up  the  plane  is  not  the 
true  force  required,  because  a  portion  of  it  is  expended  in 
overcoming  the  friction  of  the  carriage- wheels,  etc.  To 
correct  for  this  slight  excess  in  the  reading  of  the  balance, 
let  the  body  slide  down  the  plane  at  the  same  rate  of  speed 
at  which  it  was  pulled  up,  reading  the  balance  as  before. 
When  the  necessary  correction  for  the  zero  error  of  the 
balance  has  been  made,  the  average  of  the  two  readings 
will  be  very  nearly  the  true  force  required. 

Carefully  measure  the  distance  the  body  must  travel  on 
the  board  for  a  vertical  rise  of  one  foot,  ab  in  the  figure, 
or  any  vertical  distance  suitable  to  the  apparatus.  If  a 
"  T-square  "  can  be  obtained,  the  vertical  rise  taken  may 
be  marked  off  upon  one  side  of  it,  starting  from  the  outer 
edge  of  the  cross-piece.  The  T-square  is  then  placed  ver- 
tically upon  the  table  resting  against  the  board,  as  shown 
in  Fig.  90,  and  slid  along  until 
the  mark  indicating  the  vertical 
distance  coincides  with  the  lower 
edge  of  the  board.  The  distance 
from  this  point  to  the  lower  cor- 
ner of  the  board  is  the  length  of 
the  plane  to  be  measured.  If  no 
T-square  is  available,  a  plumb-line 
of  the  required  length  may  be  FlG 

dropped  from  the  lower  edge  of  the  board  and  slid  down 


172 


DYNAMICS. 


until  it  just  touches  the  table.     The  method  with  the  T- 
square  is  the  best. 

Change  the  angle  of  the  board  and  repeat  the  experi- 
ment.    Tabulate  results  as  follows: 

TABLE  I. 


Approx.  Angle 
of  Board. 

Up-force. 

Down-force. 

Vertical  Rise 
of  Body. 

Distance  on 
Plane. 

CALCULATION. — From  the  results  of  Table  I,  calculate 
and  arrange  the  data  under  the  following  headings,  where 
W=  the  weight  of  the  body,  F  =  the  true  force  required 
to  pull  the  body  up  the  plane,  Dv  =  the  distance  the  body 
was  raised  vertically,  and  Dp  =  the  distance  the  body 
moved  on  the  plane  for  this  vertical  rise. 

TABLE  II. 


w. 

F. 

Dv. 

Dp. 

QUESTIONS.—  1.  What  effect  has  the  angle  of  the  board 
on  the  force  required  to  pull  the  body  up  the  plane  ? 
2.  What  effect  has  the  angle  of  the  board  on  the  distance 
the  body  must  travel  on  the  plane  for  a  given  vertical 
rise?  3.  Can  you  make  out  any  relation  between  JFand  F 
that  also  exists  between  Dv  and  Dp  ?  4.  Calculate  for 
each  case  the  work  done  in  raising  the  body  the  given  ver- 
tical distance,  say  1  ft.,  and  the  work  done  in  raising  it  the 
same  distance  by  means  of  the  plane.*  5.  Can  any  rela- 

*  In  the  first  case,  this  equals 


and  in  the  other 

Fx  Dp. 

These  may  be  calculated  in  any  units  of  work,  but  the  same  units 
must  be  used  in  each  case.     Compare  the  values  so  obtained. 


THE  WEDGE  AND  THE  SCREW.  173 

tion  be  made  out  between  the  work  done  in  raising  a  body 
a  certain  distance  vertically  and  the  work  done  in  raising 
it  the  same  distance  by  the  plane  ?  Does  this  hold  for 
more  than  one  angle  of  the  plane  ?  6.  Does  the  machine 
save  work  ?  (i.e.,  is  less  work  done  when  the  plane  is  used 
than  when  the  body  is  lifted  vertically?)  7.  How  does  the 
machine  help  you  ? 

EXERCISE  6. 

THE  WEDGE  AND  THE  SCREW. 

Preliminary.— In  the  following  exercise  it  is  desired  to 
discover  whether  the  facts  just  observed  also  hold  when 
the  force  used  to  draw  the  body  up  the  plane  is  applied 
parallel  to  its  base,  as  in  the  wedge  and  the  screw,  instead 
of  to  its  length,  as  in  the  inclined  plane.  For  this  purpose 
the  same  apparatus  may  be  used,  the  force  being  applied 
by  pulling  the  balance  parallel  to  the  table  instead  of  to 
the  board. 

EXPERIMENT. 

OBJECT. — 1.  To  study  the  laws  of  the  wedge  and  screw. 
2.  To  see  if  the  inferences  drawn  for  the  inclined  plane 
will  hold  for  the  wedge  and  screw. 

MANIPULATION*. — Attached  to  the  front  of  the  carriage, 
C,  Fig.  89,  is  a  stick  long  enough  to  extend  beyond  the 
support  at  both  sides.  A  second  stick  of  the  same  length 
is  connected  with  the  first  by  cords,  as  shown  by  dotted 
lines,  and  the  balance  is  attached  to  the  centre  of  the 
second  stick.  As  the  connecting  cords  pass  outside  of  the 
support,  the  body  can  be  pulled  up  and  down  the  plane 
without  difficulty,  by  a  force  parallel  to  the  table.  Let  one 
student  hold  the  balance  in  both  hands,  face  up,  and  pull 
the  carriage  up  the  plane,  keeping  the  strings  parallel  to 
the  table  by  raising  his  hands  as  the  body  rises  on  the 
plane.  A  second  student  should  stand  a  short  distance 
away,  where  he  can  see  if  the  pull  is  actually  parallel  to  the 


174 


DYNAMICS. 


table.     The  students  should  alternate  in  reading  the  bal- 
ance. 

Make  the  observations,  records  and  corrections,  and 
answer  the  questions,  as  in  Ex.  5. 

EXERCISE  7. 

LAWS   OF   THE  PENDULUM. 

Preliminary.— The   apparatus  used  in  this  exercise  is 
s'  shown    in    Fig.    91.      Near    the 

edge  of  the  support  S  (which 
may  be  the  edge  of  a  table  or 
R  shelf)  is  screwed  a  spool  S'.  The 
screw  is  "  set  up  "  until  the  spool 
turns  with  considerable  friction. 
A  string  is  wound  around  the 
spool  and  is  held  in  place  by  pass- 
ing through  the  slot  of  a  screw, 
R,  inserted  horizontally  in  the 
edge  of  the  support.  The  lower 
end  of  the  string  passes  through 
a  hole  in  a  metallic  ball  B  which 
forms  the  pendulum-bob.  The 
length  of  the  pendulum  may  be 
varied  by  turning  the  spool  so  as 
to  wind  or  unwind  the  string. 
Small  adjustments  are  best  made 
Fro.  91.  by  gently  turning  the  spool. 

EXPERIMENT. 

Apparatus. — Two  iron  balls  of  different  sizes,  or  iron,  and  wooden 
balls;  apparatus  for  suspension  (screw,  spool,  fish-line);  callipers  or 
rectangular  blocks  to  get  diameters;  meter-stick;  time-piece. 

OBJECT. — To  determine  the  effect  on  the  number  of  vi- 
brations of  a  pendulum,  of  (1)  length  of  arc,  (2)  length  of 
pendulum,  (3)  weight  of  bob. 

MANIPULATION. — Part  1.  Length  of  arc.  Make  the 
length  of  the  pendulum  about  50  cm.  Count  the  number 


LAWS  Off  TBB  PMDVLUM.  175 

of  vibrations  it  makes  in  two  minutes  when  swinging 
through  an  arc  of  not  over  30  cm.  Increase  the  arc  to, 
say,  60  cm.,  the  length  of  the  swing  being  estimated  by  the 
eye.  Determine  as  before  the  number  of  vibrations  in  two 
minutes.  Compare  the  number  of  vibrations  a  minute  in 
each  case  and  draw  your  inference.  Record  the  results  as 
follows : 

TABLE  I. 


Arc. 

No.  Vibrations  in  2  min. 

No.  Vibrations  per  min. 

Long 
Short 

From  the  observation  of  the  data,  infer  the  effect  of 
length  of  arc. 

Part  2.  Length  of  pendulum.  Observe  the  general  ef- 
fect of  changing  the  length  of  the  pendulum.  Eecord 
your  observations  and  inference  in  general  terms. 

To  make  the  quantitative  determination,  we  must  com- 
pare the  number  of  vibrations  in  equal  times  of  pendulums 
of  different  measured  lengths.  The  length  of  the  pendu- 
lum is  the  distance  from  its  centre  of  gravity  to  its  point 
of  support.  The  string  having  practically  no  weight,  the 
centre  of  gravity  of  the  pendulum  corresponds  with  that 
of  the  ball,  and  is  in  the  centre  of  the  ball.  To  find  the 
length  of  the  pendulum,  therefore,  we  must  measure  the 
distance  along  the  string  from  the  lower  edge  of  the  screw 
to  the  top  of  the  ball,  and  add  to  it  half  the  diameter  of 
the  ball.  Place  the  lower  end  of  the  meter-stick  on  top  of 
the  .ball,  and  bring  its  graduated  edge  up  to  the  string. 
Measure  the  distance  to  the  edge  of  the  screw  three  times, 
reading  to  millimeters.  The  average  of  these  three  read- 
ings will  probably  be  nearly  correct.  Get  the  diameter  of 
the  ball,  where  the  hole  is,  by  placing  it  between  the  jaws 


176 


DYNAMICS. 


of  the  callipers  and  then  applying  the  callipers  to  the  scale. 
Repeat  three  times  and  average.*  The  length  of  the  string 
plus  half  the  diameter  of  the  ball  is  the  length  of  the 
pendulum. 

Set  the  pendulum  swinging  through  an-arc  of  about 
4  ins.  Measure  the  number  of  vibrations  in  1,  2,  and  3 
minutes.  Reduce  the  length  of  the  pendulum  about  half, 
measure  exactly,  and  repeat  the  counting.  Record  results 
as  follows  : 

TABLE  H. 


Length  of 
String. 

Av.  L.  of 
String. 

Diam.  of 
Ball. 

Av.  D. 

D 
2' 

True 
Length. 

No.Vib. 

Time. 

Av.  No. 
Vib. 

Part  III.  Weight  of  the  bob.  Substitute  for  the  ball 
on  the  pendulum  a  larger  ball.  Carefully  determine  the 
diameter  of  the  second  ball,  as  before.  Make  the  length  of 
the  string  such  that  the  length  of  the  pendulum  is  the 
same  as  before,  i.e.,  the  length  of  the  string  plus  the  radius 
of  the  ball  equals  one  of  the  lengths  used  in  Part  II.  De- 
termine the  number  of  vibrations  in  1,  2,  and  3  minutes  as 
before.  Record  as  in  Part  II.  Compare  the  average  num- 
ber of  vibrations  per  minute  with  that  of  similar  length  in 
Part  II. 

CALCULATION. — Divide  the  smaller  length  in  Part  II  by 
the  larger.  Divide  the  smaller  number  of  vibrations  by  the 
larger.  Compare  the  ratios  so  obtained.  If  they  do  not 
agree,  try  squaring  or  cubing  one  of  the  ratios,  and  find  the 
values  approximating  most  closely.  Infer  the  law,  and  ex- 
press it  as  a  formula. 


*  Or  use  the  method  given  in  notes  on  Mensuration. 


ACTION  AND  REACTION. 


177 


EXERCISE  8. 

ACTION  AND  REACTION. 

Preliminary. — In  this  exercise  we  experiment  with  two 
bodies  by  giving  them  various  amounts  of  energy  and 
allowing  them  to  collide.  The  special  point  of  the  experi- 
ment is  to  compare  (1)  the  energy  possessed  by  each  body 
before  and  after  the  collision,  (2)  the  energy  lost  by  one 
with  that  gained  by  the  other,  and  (3)  the  results  of  trying 
elastic  and  non-elastic  bodies.  The  apparatus  used  is  shown 


FIG.  92. 


in  Fig.  92.  Two  ivory  balls,  A  and  B,  are  so  suspended 
that  they  can  swing  in  one  plane  only,  and  will  collide  at 
the  lowest  point  of  their  arc.  They  may  be  drawn  aside 
any  desired  distance  and  held  there  by  the  electro-magnets 
CC,  and  released  by  breaking  the  circuit.  The  distances 


178  DYNAMICS. 

they  are  drawn  aside  may  be  read  on  the  scale  by  aid  of  the 
cards  bb.  The  momentum  in  each  case  is  taken  as  the 
product  of  the  weight  of  the  ball  multiplied  by  the  distance 
it  moved. 

EXPERIMENT    1. 

Apparatus.— Two  ivory  balls;  No.  30  wire;  electro-magnets;  board; 
two  meter-sticks;  electric  current;  circuit-breaker;  tacks;  made  into 
apparatus  as  shown;  scales  and  weights  (if  balls  are  not  of  known 
weight). 

OBJECT. — To  compare  (1)  the  algebraic  sums  of  the  ener- 
gies possessed  by  two  bodies  before  and  after  collision,  (2) 
the  results  of  trying  elastic  and  non-elastic  bodies,  (3)  the 
direction  of  the  action  and  reaction,  (4)  the  energy  lost  -by 
one  with  that  gained  by  the  other. 

MANIPULATION". — A  little  adjustment  of  the  magnets  as 
regards  their  position  in  the  plane  of  oscillation  will  enable 
the  student  to  release  the  balls  so  that  they  will  strike 
squarely  upon  each  other.  By  means  of  the  index-cards  cc, 
determine  on  the  meter-stick  the  position  of  the  balls  when 
at  rest.  One  ball  being  at  rest,  place  the  magnet  so  as  to  hold 
the  other  ball  about  10  or  15  cm.  aside.  Kead  the  position 
of  this  ball  by  the  index-card  b.  Break  the  circuit,  thus 
allowing  one  ball  to  strike  the  other,  and  notice  the  dis- 
tance traversed  by  each  ball  after  collision.  Place  an  index- 
card  at  each  of  these  points,  and  repeat  the  experiment. 
Sighting  across  each  index,  note  the  exact  position  reached 
by  the  centre  of  the  corresponding  ball,  and  place  the  index 
at  this  point.  Try  again  until  each  index  marks  the  exact 
position  reached  by  centre  of  the  corresponding  ball  after 
collision.  As  the  magnet  remains  in  the  same  place  all  the 
time,  the  distance  traversed  by  the  ball  before  collision  is 
always  the  same,  and  need  not  be  measured  again.  Follow- 
ing this  method,  try  the  following  cases,  calling  the  small 
ball  By  and  the  large  ball  A  : 

Case  1.  A  in  motion,  B  at  rest.  Try  two  cases,  and  re- 
peat with  B  in  motion  and  A  at  rest. 


ACTION  AND  REACTION. 


179 


.  Eelease  both  balls  at  once.  Try  covering  one 
ball  with  a  thin  layer  of  putty.  The  weights  of  the  balls 
should  be  determined  in  each  case. 

Compare  the  momenta  before  and  after  collision  in  each 
case.  Distinguish  between  the  behavior  of  elastic  and  in- 
elastic substances  under  these  circumstances.  In  calculat- 
ing the  momenta,  call  the  movement  towards  the  right 
hand  -f,  towards  the  left  hand  — .  Tabulate  results  as 
follows : 

Weight  of  A...  Weight  of  B.... 


l 


.  tra 
ter  c 


ed 
coll 


From  the  above  data  calculate  the  momenta  before  and 
after  collision  in  each  case,  being  careful  to  keep  the  proper 
signs.  Arrange  results  as  follows  : 

Case  1.     Momentum  of  A  before  collision  = 
"  "  A  after          "       = 

"  «  B  before        "       = 

"  «  B  after          "       = 

Algebraic  sum  = 

From  these  data  answer  the  questions  given  in  the  object. 

SUBSTITUTE    EXPERIMENT. 

Apparatus.— Two  pint  tin  pails,  suspended  and  adjusted  as  shown; 
heavy  bodies  to  load  pails;  cotton  string;  candle;  two  meter-sticks; 
coarse  scales. 

OBJECT. — (1)  To  compare  the  values  of  action  and  re- 
action when  two  bodies  are  acted  upon  by  the  same  force, 
and  (2)  to  study  the  effect  of  varying  the  weight  of  the 
bodies, 


180 


DYNAMICS. 


MANIPULATION. — Set  up  the  apparatus  as  shown  in  Fig. 
93.  Call  the  pail  with  the  spring  A,  and  the  other  B. 
Detach  B  from  the  wires,  and  make  it  weigh  250  grams 
(cover  on).  Compress  the  spring  and  tie  it  with  a  string.* 


FIG.  93. 

In  the  same  way  make  A  weigh  500  grams.  Attach  both 
the  pails  to  the  wires,  being  sure  that  they  hang  vertically. 
Holding  the  eye  directly  above  the  outer  edge  of  each  pail 
in  turn,  read  its  position  on  the  meter-stick  underneath, 
and  record.  Now  place  a  meter-stick  under  the  edge  of 
each  pail,  and  burn  the  string.  As  the  pails  swing  out 
keep  a  pencil  directly  under  the  outer  edge  of  each  one, 
and  stop  them  at  the  extreme  point  of  the  swing.  While 
the  pails  return,  hold  the  pencils  steady  at  these  points, 
read  their  positions  on  the  meter-sticks,  and  record.  Re- 
peat three  times;  then  make  pail  B  500  grm.,  and  try  again, 
say  three  times  more.  If  possible,  try  again  with  750  grm. 
Tabulate  results  as  follows : 

*  It  is  a  good  plan  to  hold  the  hand  between  the  pails  when  they 
come  together,  so  that  they  will  not  strike  each  other  with  a  heavy 
blow. 


THE  FORGE  OF  TENACITY. 


181 


TABLE    I. 


Wt.  A. 

Wt.  B. 

Read.  A 
at  rest. 

Read.  B 
at  rest. 

Read.  A 
at  end  of 
swing. 

Read.   B 
at  end  of 
swing. 

From  the  data  in  Table  I  calculate  the  following  table: 

TABLE  II. 


Wt.  A. 

Wt.  B. 

Dist.  A  moved. 

Dist.  B  moved. 

Wt.  A  x 
Dist.  A. 

Wt.  B  x 
Dist.  B. 

QUESTIONS. — 1.  Can  any  relation  be  made  out  between 
the  weights  of  the  pails  and  the  distances  that  they  moved  ? 
2.  What  relations  appear  between  the  numbers  in  the  last 
two  columns  in  Table  II?  3.  Calling  w  and  W  the 
weights  of  the  two  pails,  and  d  and  D  the  distances  moved, 
can  the  results  be  expressed  as  a  formula  ?  4.  Can  any 
law  be  inferred  for  the  relation  of  action  and  reaction  re- 
garding (a)  direction,  (b)  extent  of  motion  ? 

EXERCISE  9. 

THE  FORCE  OF  TENACITY. 

EXPERIMENT. 

Apparatus.— Wire  of  two  sizes  and  two  materials;    half -spool 
screwed  to  table;  24-lb.  spring-balance;  meter-stick. 

OBJECT. — To  study  the  effect  of  length,  cross-section, 
and  material  on  the  force  of  tenacity. 

MANIPULATION. — Part  I.  Effect  of  Length.  Pass  one 
end  of  the  wire  twice  around  the  half-spool  with  a 
"round  turn,"  making  it  lie  close  to  the  spool  all  the  way; 
then  twist  the  end  of  the  wire  around  its  main  part,  as 


182 


DYNAMICS. 


indicated  in  Fig.  94. 


FIG.  94. 


The  spool  is  screwed  to  the  table. 
Cut  off  the  wire  about 
one  meter  from  the  spool, 
and  attach  the  end  to  the 
balance-hook,  precisely 
as  shown  in  Fig.  94.  Ex- 
amine the  wire  to  make  sure  that  it  is  free  from  "  kinks/7 
and  measure  its  length.  Then,  holding  the  balance  hori- 
zontally in  the  palm,  move  the  hand  along  with  its  back 
on  the  table  so  as  to  produce  a  steady  pull  on  the  wire. 
Steadily  increase  the  pull  until  the  wire  breaks,  meantime 
watching  the  index  of  the  balance  all  the  time  so  as  to 
know  where  it  stands  when  the  wire  breaks.  The  first 
trial  will  tell  about  what  part  of  the  scale  to  watch  in  sub- 
sequent trials.  Make  four  trials  besides  the  first,  and  try 
to  read  to  £  lb.,  especially  in  the  third  and  fourth  trials. 
Take  a  different  length  for  each  trial,  and  record  the 
length  of  each  piece. 

Part  II.  Effect  of  Cross-section.  In  the  same  manner 
determine  the  tenacity  of  the  second  size  of  wire,  making 
four  trials. 

Part  III.  Effect  of  Material.  Determine  in  the  same 
way  the  tenacity  of  the  wires  of  different  material,  making 
four  trials. 

Tabulate  results  as  follows : 


No.  Trial. 

Length  of  Wire. 

Cross-section. 

Bk.Wt.  on  Bal. 

Correct  Bk.Wt. 

The  values  in  the  last  column  are  the  balance-readings 
corrected  for  zero  and  position  errors. 

QUESTIONS. — 1.  Can  you  make  out  any  relation  between 
length  and  tenacity  ?  2.  Between  cross-section  and  tenac- 
ity ?  3.  Has  material  any  effect  ?  4.  What  cross-section 


THE  FORCE  OF  ELASTICITY. 


183 


E 


of  one  wire  would  give  the  same  tenacity  as  another  wire 
of  different  cross-section  and  material  ? 

EXERCISE  10. 

THE  FORCE  OF  ELASTICITY. 

Preliminary. — A  body  whose  shape  has  been  changed  by 
the  action  of  a  force  is  said  to  be  distorted.  A  body  which 
tends  to  take  its  former  shape  when  distorted  is  said  to  be 
elastic.  The  force  with  which  a  distorted  elastic  body 
tends  to  resume  its  original  shape  is  called  the  force  of  elas- 
ticity. A  body  which  may  be  considerably  distorted  with 
very  little  force  is  said  to  be  very  elastic,  or  to  have  low 
elasticity.  Rubber  is  an  example  of  low  elasticity.  A  body 
which  gives  considerable  force  of  elasticity  on  small  distor- 
tion is  said  to  have  high  elasticity.  Steel  is  an  example  of 
high  elasticity.  The  following  exercise 
investigates  the  effect  of  (1)  degree  of 
distortion,  (2)  cross  -  section,  and  (3) 
length  on  the  magnitude  of  the  force  of 
elasticity  in  a  solid.  For  this  purpose 
the  apparatus  in  Fig.  95  is  used.  The 
rubber  strip  S  is  fastened  at  its  upper 
end,  and  may  be  stretched  (distorted)  by 
weights  placed  in  the  scale-pan  E,  which 
is  attached  to  its  lower  end.  Since,  after 
the  strip  has  stretched  and  is  at  rest,  the 
up  pull  due  to  the  elasticity  of  the  rub- 
ber, and  the  down  pull  due  to  the  weights, 
must  be  equal,  the  weights  measure  the 
force  of  elasticity.  The  total  amount  of 
distortion  is  measured  by  reading  the 
position  of  the  point  a  on  the  meter-stick, 
by  means  of  the  reading-card  C.  The 
distortion  of  two  lengths,  one  twice  the 
other,  may  be  compared  by  reading  first 
from  the  point  a,  and  then  from  point  b.  The  position  of 


FIG.  95. 


184  DYNAMICS. 

the  card   C  may  be  changed  by  slipping  off  the  rubber 
bands  RR,  and  sliding  it  along  the  meter-stick. 


EXPERIMENT. 

Apparatus.— Apparatus  for  the  experiment  as  shown  ;  weights  10 
to  200  g. ;  screw -driver. 

OBJECT. — (1)  To  see  if  any  relation  can  be  found  between 
the  amounts  of  distortion  of  an  elastic  body  and  the  cor- 
responding magnitudes  of  the  force  of  elasticity.  (2)  To 
observe  the  effect  (a)  of  cross-section,  (b)  of  length. 

MANIPULATION. — Part  I.  Adjust  C  so  that  the  upper 
edge  of  the  card  touches  the  lower  edge  of  the  mark  a  on 
the  rubber  strip.  Hold  it  there  by  hand  or  by  the  rubber 
bands,  and  read  and  record  the  position  of  the  upper  edge 
of  the  card  on  the  meter-stick.  Gently  place  20  gr.  on  the 
scale-pan,  and  after  the  strip  has  come  to  rest,  again  adjust 
C,  and  read  the  position  of  a  and  record.  Eepeat  with  40 
gr.  in  the  pan,  and  so  proceed  for  ten  readings  in  all  (up  to 
200 gr.).  Eecord  as  follows: 


Weight  used. 

Position  of  a. 

Distortion  of  S.* 

Part  II.  Eepeat  Part  I,  reading  from  b,  and  record  in 
the  same  way. 

Part  III.  Detach  the  strip  used  in  Part  II,  and  substi- 
tute the  wide  one.  Eepeat  with  this  strip.  When  read 
from  the  mark  upon  it,  this  gives  the  same  length  and 
cross-section  as  the  one  in  Parts  I  and  II. 

QUESTIONS. — What  effect  have  length  and  cross-section  ? 
2.  Are  all  bodies  equally  elastic  ?  (Answer  from  your  gen- 

*  The  position  of  a  for  each  weight  minus  that  for  no  weight. 


BOYLE'S  LAW. 


185 


eral  knowledge.)  3.  What  conditions  have  you  found  to 
affect  the  magnitude  of  the  force  of  elasticity  ?  Plot  a  cure 
from  the  data  of  Part  I. 

EXERCISE  11. 

BOYLE'S  LAW. 

Preliminary. — We  know  that  when  pressure  is  exerted 
on  a  confined  volume  of  gas  its  volume  becomes  less,  and 
that  when  the  pressure  is  diminished  the  volume  increases. 
In  the  following  exercise  we  wish  to  see  if  we  can  find  any 
relation  between  different  pressures  and  the  corresponding 
volumes.* 

The  apparatus  used  is  shown  in  Fig.  96.  A  glass  tube,  ab, 
is  bent  as  shown.  The  short  arm  is  closed  at  the  top,  the 
long  arm  open.  The  gas  to  be 
experimented  upon  is  confined 
at  b  in  the  short  arm  by  pour- 
ing mercury  into  the  long  arm. 
The  pressures  can  be  changed 
by  using  different  depths  of 
mercury,  the  volume  of  gas 
can  be  read  on  the  scale  d,  and 
the  depths  of  mercury  on  the 
scales  d  and  e.  The  two  cards 
ff  help  in  reading  the  levels. 
As  we  know  from  the  laws  of 
liquid  pressure,  the  depth  of 
mercury  causing  the  pressure 
will  be  the  difference  in  the 
heights  of  the  two  columns; 
and  since  the  atmospheric  CZ 
pressure  is  exerted  on  the  top 
of  the  column  in  «,  the  total  pressures  will  equal  the 


FIG.  96. 


Suggest  a  method  for  such  an  experiment. 


186  DYNAMICS. 

height  of  mercury,  causing  the  pressure  plus  the  height 
of  the  barometer,  whose  reading  must  be  known.  Since 
changes  of  temperature  affect  the  volume,  the  tempera- 
ture must  be  practically  uniform  during  the  exercise. 

EXPERIMENT. 

Apparatus.—  As  shown  (tube;  support;  scales;  reading-cards); 
about  500  gr.  mercury  (clean  and  dry);  barometer;  feather  and  rod 
to  remove  air. 

OBJECT.  —  To  discover  some  relation  between  the  volume 
of  a  confined  body  of  gas  and  the  pressure  exerted  upon  it. 

MANIPULATION".  —  Eead  the  barometer.  (See  the  card 
of  instructions  tacked  over  the  instrument,  with  instruc- 
tions for  reading  vernier,  etc.)  The  barometer  reads  in 
inches;  as  the  other  readings  will  be  in  centimeters,  con- 
vert the  barometer-reading  to  centimeters  by  the  following 
formula  : 

Bar.  -read,  in  inches      ^  ,    . 

~  Bar.  -read,  in  cm. 


Eead  the  thermometer.  Place  the  glass  funnel  (be  sure 
that  it  is  clean  and  dry)  in  the  open  end  of  the  long 
arm,  and  carefully  pour  in  mercury  until  the  bend  is  cov- 
ered and  the  mercury  stands  two  or  three  cm.  higher  in  the 
long  arm  than  in  the  short  arm.  Tip  to  the  left  the  appa- 
ratus as  it  stands  in  Fig.  96,  and  allow  some  air  to  escape 
from  the  short  arm;  place  the  apparatus  upright  again, 
note  the  levels,  and,  if  necessary,  repeat  until  the  mercury 
stands  at  about  the  same  level  in  both  arms.  If  the  level 
of  the  mercury  in  the  short  arm  is  still  below  the  upper 
edge  of  the  horizontal  part  of  the  tube,  add  a  little  more 
mercury.  If  too  much  air  has  been  allowed  to  escape,  tip 
the  apparatus  to  the  right  and  let  some  air  run  in.  Work- 


BOYLE'S  LAW.  187 

ing  in  this  way,  get  the  level  of  the  mercury  in  the  short  arm 
above  the  curve,  and  the  mercury  in  the  long  arm  from  1 
to  3  cm.  higher.  Then  read  the  position  of  the  top  of  the 
meniscus  of  each  mercury-column  on  its  scale.  Place  the 
funnel  again  in  the  top  of  the  tube,  and  carefully  pour  in 

'ercury  until  the  level  of  the  column  in  the  long  arm  has 
m  raised  about  15  cm.  Eemove  the  air-bubbles  and 

,ain  read  the  heights  in  both  arms  on  the  scales.  With 
uae  same  precautions  add  another  15  to  20  cm.  height  to 
the  long-arm  column.  Again  read  the  levels.  So  proceed 
till  the  difference  in  the  levels  of  the  columns  in  the  two 
arms  is  about  75  to  85  cm.  Again  read  the  barometer,  and 
if  you  find  any  difference  in  the  barometer-readings  before 
and  after  these  operations,  use  the  average  of  the  two. 
Read  the  thermometer,  and  if  you  find  a  small  change  in 
temperature,  average  the  readings;  if  a  large  change,  report 
the  fact  at  once.  During  the  progress  of  the  experiment, 
watch  the  thermometer  and  note  any  change  of  tempera- 
ture. Now  you  have  the  following  data : 

(a)  Barometer-reading  before  and  after. 

(b)  Thermometer-reading  before  and  aftei 

(c)  Levels  of  mercury  in  the  short  arm. 

(d)  "      "        "         "    "  long     " 

Arrange  (c)  and  (d)  in  a  table  as  follows: 

TABLE  I. 


Height  in  Short  Arm. 

Height  in  Long  Arm. 

No.  Trial. 

188 


DYNAMICS. 


CALCULATION. — Arrange  the  results  of  the  calculation  in 
a  table  of  five  columns,  as  follows : 


TABLE  II. 


Volumes. 

Pressure. 

Whole  Press. 

Ratios  of  Vol. 

Ratios  of  Press. 

The  figures  in  column  1  are  obtained  from  the  card 
attached  to  the  apparatus,  the  volumes  in  cubic  centi- 
meter corresponding  to  each  reading  on  the  short-arm 
scale,  The  higher  the  number  on  the  scale  the  less  the 
volume  of  air  represented.  The  figures  in  column  2  are 
obtained  by  subtracting  the  readings  of  the  short  arm  from 
those  of  the  long  arm.  The  figures  in  column  3  are  ob- 
tained by  adding  to  each  number  in  the  second  column  the 
height  of  the  barometer  in  centimeters.  This  gives  the 
total  pressure  of  mercury  in  centimeters.  The  figures  in 
column  4  are  obtained  by  dividing  each  volume  in  turn  by 
the  smallest  volume.  The  figures  in  column  5  are  obtained 
by  dividing  each  pressure  (column  3)  in  turn  by  the  small- 
est pressure.  Carry  out  both  these  ratios  to  the  second 
place  of  decimals. 

QUESTIONS. — 1.  Is  there  any  law  as  regards  the  ratio  of 
the  volume  to  the  pressure  of  a  gas,  the  temperature  being 
constant  ?  2.  If  so,  what  is  it  ?  3.  Why  read  the  barome- 
ter twice  ?  4.  Why  read  the  thermometer  twice  ?  5.  What 
keeps  the  mercury  from  completely  filling  the  small  arm  ? 
6.  Is  it  of  the  nature  of  a  push?  7.  Is  it  a  force?  8.  What 
is  the  name  of  that  force  ?  9.  In  this  experiment  what  is 
the  stress?  10.  In  this  experiment  what  is  the  strain? 
11.  What  sort  of  elasticity  has  a  gas  ?  12.  What  princi- 


SPECIFIC  GRAVITY  WITHOUT  SCALES  OR  WEIGHTS.  189 

pies,  learned  in  previous  experiments,  have  you  made  use 
of  in  this  one  ?    Plot  a  curve  from  the  data. 


EXERCISE   12. 

SPECIFIC  GRAVITY  WITHOUT  SCALES  OR  WEIGHTS. 

EXPERIMENT    1. 

Apparatus.— Suspended  meter-stick;  two  stones  or  other  bodies 
of  about  equal  weight;  cords;  vessel  of  water. 

OBJECT. — To  determine  the  specific  gravity  of  a  solid  by 
the  principle  of  moments. 

MANIPULATION. — Call  the  body  whose  specific  gravity  is 
to  be  determined  A,  and  the  other  B.  Suspend  A  about 
25  cm.  from  end  of  the  meter-stick,  Fig.  97,  having  the 
loop  of  the  suspending 
string  tight  enough  not  to 
slip  during  the  experiment, 
Slide  the  weight  along  un- 
til it  balances  A,  and  note 
its  distance  from  the  sup- 
port S.  Bring  a  vessel  of 
water  under  A,  and  when 
A  is  completely  submerge*!, 
and  clear  of  the  sides  ana 
bottom  of  the  vessel,  move 
B  until  it  balances  it  again,  and  note  its  distance  from  S. 
You  have  now  the  data  for  determining  the  specific  gravity 
of  A. 

CALCULATION. — In  Fig.  97  aS  represents  the  weight  in 
air,  bS  represents  the  weight  in  water;  so  aS  —  bS  or  ab 

represents  the  loss  of  weight,  and  specific  gravity  =  — j-. 


100 


DYNAMICS. 


EXPERIMENT    2. 

Apparatus.— Long  spiral  spring;  meter-stick;  clamp;  body  whose 

specific  gravity  is  to  be  deter- 

A  B  G  mined ;  vessel  of  water;  string 

or  wire. 

OBJECT. — To  determine  the 
specific  gravity  of  a  solid  body. 

MANIPULATION.  —  Note 
length  of  spring,  with  sus- 
pended wire  only  attached, 
Fig.  98,  0.  Attach  the  body 
to  the  lower  end,  as  in  Fig.  98, 
A,  and  record  the  length  of 
spring.  Bring  the  vessel  of 
water  under  the  body,  immerse 
the  body  with  the  usual  pre- 
cautions, and  again  record  the 
length  of  the  spring  B. 

CALCULATIONS. — Reading  of 
reference-marks : 

Spring  alone  = 

With  body  attached  = 

Body  immersed         = 

ac  represents  wt.  in  air. 

ab        "  "    "  water,  and 

ac  —  ab  represents  loss  of  wt. 

in  water,  and 
Specific  gravity  = 


PIG.  98. 


ac      _  ac 
ac  —  ab      be 
In  same  way  find  specific  gravity  of  some  liquid. 


LIGHT. 


EXERCISE  1. 

FOCI  OF  LENSES. 

Preliminary.— When  the  light  from  a  luminous  body 
passes  through  a  double  convex  lens,  the  point  at  which 
all  the  light  is  concentrated  is  called  the  focus  of  the  lens. 
The  distance  from  the  centre  of  the  lens  to  the  focus  is 
called  the  focal  length.  The  following  exercise  investigates 
the  effect  on  the  focal  length  of  the  distance  of  the  object 
from  the  lens.  The  apparatus  shown  in  Fig.  99  is  used. 


s 

^ 

<0 

A 

JUJ-L 

^uuu^ 

fZ 

FIG.  99. 

For  the  luminous  object  near  the  lens  we  use  a  light  A, 
represented  as  a  candle  mounted  upon  a  block  C",  which 
slides  upon  the  meter-stick  M.  The  lens  L  and  the  screen 
8  are  similarly  arranged.  The  position  of  the  lens  can  be 
so  adjusted  that  the  image  of  A  falls  on  S  when  A  is  at 
different  distances  from  the  lens,  and  the  distances  AL  and 
L8  can  be  read  on  the  meter-stick. 

EXPERIMENT. 

Apparatus.— As  in  Fig.  99,  so  arranged  that  an  image  of  an  object 
at  a  considerable  distance  may  be  obtained. 

OBJECT. — To  study  the  effect  of  the  distance  of  the  ob- 
ject from  the  lens  on  its  focal  length. 

191 


192 


LIGHT. 


MANIPULATION'. — Bring  the  outer  ends  of  blocks  C  and 
G"  even  with  the  ends  of  the  meter-stick.  Light  A,  place 
it  in  the  centre  of  block  C",  and  move  the  lens  to  a  point 
about  20  cm.  from  A.  Slowly  slide  the  block  G'  towards 
S  until  a  position  is  found  which  gives  a  sharp  image  of 
A  on  the  screen.  Eecord  the  readings  of  the  right-hand 
sides  of  S  and  D  and  of  block  C"  (in  this  case,  0).  Move 
the  lens  towards  8  until  the  image  is  lost,  then  slowly  move 
it  back  towards  A  until  a  sharp  image  is  again  obtained, 
and  take  the  reading  of  D  as  before.  Gently  slide  block 
C"  10  cm.  nearer  the  lens,  and  repeat.  So  continue  at  in- 
tervals of  10  cm.  until  an  image  can  no  longer  be  obtained. 
To  test  the  case  when  the  object  is  as  far  from  the  lens  as 
possible,  extinguish  the  light  and  remove  it,  together  with 
block  C".  Arrange  the  rest  of  the  apparatus  so  that  the 
light  from  some  distant  object  *  can  pass  through  the  lens 
and  fall  upon  the  screen.  Find  as  above  the  position  of 
D  that  gives  a  sharp  image.  Kecord  as  follows: 

TABLE  I. 


Bead,  of  8. 

Read,  of  D. 

Read,  of  A. 

R. 

L. 

Av. 

In  the  first  and  third  columns  place  the  readings  of  right- 
hand  sides  of  C"  and  8,  respectively.  In  the  second  col- 
umn R  and  L  are  the  readings  of  the  right-hand  side  of  D 
when  moved  from  the  right  or  from  the"  left  to  the  posi- 
tion giving  a  sharp  image. 

QUESTIONS. — 1.  Is  the   distance  of  the  lens  from  the 

*  The  distance  of  this  object,  which  should  be  over  30  meters  from 
the  lens,  should  be  recorded,  whether  measured  or  estimated  by  the 
eye. 


FOCI  OF  LENSES. 


193 


screen  the  same  whatever  the  distance  of  the  luminous 
object  from  the  lens?  2.  What  other  inferences  can  you 
draw  from  the  results  of  the  experiment  ? 

When  the  object  is  so  distant  that  the  rays  of  light  from 
it  are  practically  parallel  where  they  strike  the  lens,  as  in 
the  case  of  the  distant  object  in  the  experiment,  the  dis- 
tance from  the  centre  of  the  lens  to  the  image  is  called  the 
true  focal  length  of  the  lens.  When  the  object  is  so  near 
the  lens  that  the  rays  of  light  are  not  parallel,  this  distance 
is  called  the  conjugate  focal  length. 

CORRECTIONS. — In  order  to  make  any  exact  comparisons, 
it  is  necessary  that  the  true  positions  of  A  and  of  the  lens 
should  be  determined.  To  get  the  true  position  of  A,  add 
one  half  the  length  of  block  C"  to  the  readings  of  A  in 
Table  I.  For  the  position  of  the  centre  of  the  lens  add 
one  half  the  width  of  the  board  D  to  the  average  readings 
for  D  in  the  same  table.  Eecord  as  follows  : 

TABLE  II. 


True  pos.  A. 

True  pos.  L. 

Pos.  8. 

Dist.  AL. 

Dist.  LS. 

CALCULATION.  —  Taking  the  first  case,  express  the  frac- 
tion -r-j  as  a  decimal  carried  out  to  four  significant  fig- 


ures.    Express  the  fractions  ^-^  and  ^  —  T-^  -  —  *  in  the 

LS  Focal  length 

same  way.     Do  the  same  for  the  other  cases.     Tabulate  as 
follows  : 


*  As  obtained  in  the  trial  with  the  distant  object. 


194                                  LIGHT. 

TABLE  in. 

1 

1 

1 

AL 

Ta 

Sum  of  the  two. 

F.L. 

QUESTIONS. — 1.  From  the  study  of  Table  III  can  you 
make  out  any  relation  between  the  distance  of  the  object 
from  the  lens  (AL),  the  conjugate  focal  length  (LS),  and 
the  true  focal  length  of  the  lens  ?  If  so,  letting  F  —  true 
focal  length,  /=  conjugate  focal  length,  arid  D  =  the  dis- 
ance  of  the  object  from  the  lens,  express  your  inference  as 
a  formula. 

EXERCISE  2. 

DISTANCE  AND  INTENSITY  OF  LIGHT. 

Preliminary. — By  the  intensity  of  light  is  meant  not  the 
brightness  of  the  source  of  light  itself,  as  a  lamp-flame, 
white-hot  carbon,  etc.,  but  the  degree  to  which  its  light 
illuminates  a  given  body.  It  is  a  well-known  fact  that  the 
illuminating  power  of  a  light  decreases  as  the  distance  of  the 
illuminated  body  from  it  increases.  The  light  from  a  large 
lamp  and  from  a  candle  may  be  of  equal  intensity  if  the  il- 
luminated body  be  much  nearer  to  the  candle  than  to  the 
lamp.  The  following  exercise  investigates  the  effect  of  dis- 
tance on  intensity  of  light,  with  a  view  to  seeing  if  any  fixed 
relation  can  be  made  out  between  them.  In  order  to  do 
this,  we  determine  the  distances  at  which  lights  of  different 
known  powers  give  light  of  the  same  intensity.  For  this 
purpose  we  use  an  instrument  called  a  Bunsen  Photometer, 
whose  operation  is  based  upon  the  fact  that  when  a  piece  of 
paper  having  a  paraffin  e  spot  in  the  centre  is  equally  lighted 
on  both  sides,  the  spot  can  no  longer  be  seen.  The  form 
used  is  shown  in  Fig.  100.  The  lights  are  placed  upon  the 


DISTANCE  AND  INTENSITY  OF  LIGHT.         195 

blocks  C  and  E  and  the  paper  upon  the  block  B.  All  the 
blocks  slide  upon  the  meter-stick.  For  lights  of  different 
intensities  we  use  different  numbers  of  candles,  assuming 
that  two  candles  give  twice  as  powerful  a  light  as  one. 
Taking  lights  of  different  intensities,  and  finding  the  dis- 


Fia.  100. 

tance  from  each  light  to  the  paper  when  the  paper  has 
been  placed  so  that  the  spot  in  its  centre  is  no  longer  visi- 
ble, we  have  the  distances  required  for  the  different  lights 
to  give  the  same  degree  of  intensity. 

EXPERIMENT. 

Apparatus  —  Bunsen  photometer,  as  in  Fig.  100;  5  candles,  3  or  4 
in.  long;  matches;  scissors  for  trimming  candle-wicks. 

OBJECT. — To  see  what  relation  exists  between  the  intens- 
ity of  a  light  and  its  distance  from  the  lighted  object. 

MANIPULATION. — Arrange  blocks  C  and  E  at  the  ends 
of  the  meter-stick,  as  in  the  preceding  exercise.  Place 
one  lighted  candle  on  the  block  C  and  one  on  block  E. 
Move  the  block  B  towards  Gy,  watching  it  from  that  side 
until  the  spot  shows  plainly;  then  slowly  move  it  away 
until  the  spot  just  disappears.  Have  the  eye  about  level 
with  the  spot,  and  the  line  of  sight  at  an  angle  of  about 
30°  with  the  meter-stick.  If  possible,  shield  the  eye  from 
the  direct  light  of  the  candles  by  card-board  screens.  Head 
the  position  of  the  right-hand  side  of  D.  Next  looking  at 
A  from  the  left-hand  side,  move  B  within  20  cm.  of  E\ 
then  back  towards  C  until  the  spot  just  disappears.  Ee- 
cord  the  reading  of  D.  Move  B  within  20  cm.  of  C,  and 
again  determine  the  position  where  the  spot  is  invisible 
when  looked  at  from  the  right-hand  side,  as  in  the  first 
case.  Working  in  this  way  from  each  side  alternately, 


196 


LIGHT. 


make  about  ten  readings  in  all.  During  the  operation  keep 
the  candle-flames  burning  evenly,  trimming  the  wicks  if 
necessarj7.*  In  order  that  the  effect  of  a  variation  in  flame 
may  be  still  more  reduced,  it  is  advisable  to  change  the 
candles  end  for  end  of  the  apparatus,  moving  blocks  and 
all.  If  this  be  done,  take  twelve  readings  in  all.  Repeat 
these  readings  first  with  two  and  then  with  four  candles  on 
C,  setting  the  candles  about  1  cm.  apart  in  a  line  at  right 
angles  to  the  length  of  the  meter-stick.  Tabulate  results 
as  follows: 

TABLE  I. 


Reading  of  B. 

Pos.  of  Centre  of  L. 

Pos.  of  Centre  of  L'. 

R. 

L. 

Av. 

CALCULATION. — The  readings  for  B  are  practically  cor- 
rect. The  positions  of  the  centres  of  the  candles  are  found 
as  in  the  preceding  exercise.  Record  corrections  as  follows: 


TABLE  II. 


Inten.  of  L.t 

Inten.  of  Z/.t 

Dist.  LD. 

Dist.  L'D. 

The  numbers  in  the  last  two  columns  are  the  distances 
from  the  centres  of  the  candles  to  D. 

QUESTIONS. — 1.  How  would  the  distances  compare  if 
nine  candles  were  used  ?  Sixteen  ?  Twenty-five  ?  2.  Can 
you  make  out  any  uniform  relation  between  the  distances 

*  To  protect  the  caudles  from  draughts,  lamp-chimneys  may  be 
placed  over  them,  supported,  of  course,  so  that  air  may  enter  from 
the  bottom. 

f  That  is,  number  of  candles  used  in  each  case. 


RADIATION  OF  LIGHT.  197 

and  the  intensities  ?  If  so,  using  /  and  /'  for  the  intensi- 
ties and  D  and  D'  for  the  distances,  express  your  inference 
as  a  formula. 

EXERCISE  3. 

RADIATION  OF  LIGHT. 

Preliminary. — It  is  generally  known  that  light  radiates, 
or  spreads  out  in  every  direction,  from  a  luminous  point. 
The  following  exercise  investigates  the  effect  of  distance 
from  the  light  upon  the  degree  of  radiation.  The  light 
from  a  luminous  body  is  allowed  to  pass  through  a  small 
opening,  and  the  degree  to  which  it  spreads  is  determined 
by  letting  it  fall  upon  a  screen  whose  distance  from  the 
light  may  be  varied. 

In  order  that  the  light  should  radiate  from  as  nearly  a 
point  as  possible,  the  light  is  placed  in  a  box  with  a  small 
hole  opposite  the  flame  on  the  side  towards  the  screen. 

EXPERIMENT. 

Apparatus.—  As  in  Fig.  99,  the  lens  being  removed  and  a  piece  of 
paper  with  a  hole  2  cm.  square  tacked  over  the  hole  in  Z>;  a  box 
fitted  to  hold  the  light;  a  short  mm.  scale;  sharp  pencil;  some  pieces 
of  writing-paper  about  3x3  in.,  one  of  which  is  pinned  on  the  screen 
at  the  beginning  of  the  exercise. 

OBJECT. — To  see  if  there  is  any  uniform  relation  between 
the  degree  of  radiation  and  the  distance  from  the  point  of 
radiation. 

MANIPULATION.— Light  the  candle  and  adjust  the  block 
supporting  it  so  that  the  reading  of  the  opening  in  the  box 
through  which  the  light  passes  is  5  or  10  cm.  on  the  scale.* 
Place  D  25  cm.  and  8  35  cm.  from  the  hole.  If  the  light 
is  properly  adjusted,  a  well-defined  square  of  light  will  be 
thrown  on  the  screen.  Holding  the  screen  firmly,  place  a 
ruler  upon  it,  and  with  a  sharp  pencil  rule  a  vertical  line  2 

*  One  method  of  doing  this  would  be  to  hold  the  ruler  firmly 
against  the  side  of  the  box  facing  the  screen,  and  adjust  so  that  the 
right-hand  edge  of  the  ruler  would  come  on  the  5  or  10  cm.  mark 
on  the  meter- stick. 


198 


LIGHT. 


or  3  cm.  long  on  the  left-hand  edge  of  the  square  of  light, 
using  great  care  to  get  the  lines  exactly  on  the  edge. 
Mark  the  right-hand  edge  in  the  same  way.  Set  the  screen 
40  cm.  from  the  hole,  and  rule  two  more  lines.  So  proceed 
up  to  60  cm.  from  the  hole.  Remove  the  square  of  paper 
pinned  on  the  screen,  pin  on  a  fresh  square  and  get  an- 
other set  of  lines,  working  back  from  60  to  35.  Get  four 
sets  of  lines  in  all,  working  back  and  forth  twice.  Meas- 
ure carefully  on  all  four  pieces  of  pieces  of  paper  the  dis- 
tance between  the  pairs  of  lines  obtained  for  each  position 
of  the  screen.  Record  as  follows : 

TABLE  I. 


Pos.  of  Point. 

Pos.  of  Screen. 

Dist.  between  Lines. 

1st. 

2d. 

3d. 

4th. 

Av. 

v 

From  these  results  calculate 

TABLE  n. 


Dist.  from  Point 
to  Screen. 

Increase. 

Av.  Width  of 
Square  of  Light. 

Increase. 

In  the  first  column  place  the  reading  of  the  screen 
minus  the  reading  of  the  left-hand  side  of  the  box.  The 
figures  in  the  second  column  are  obtained  by  getting  the 
differences  between  the  different  readings  of  the  screen. 
In  the  third  column  place  the  average  values  obtained  from 
Table  I  for  the  distance  between  the  pairs  of  lines  corre- 
sponding to  each  position  of  the  screen,  and  in  the  fourth 
column  obtain  the  differences  in  the  same  way  as  indicated 
for  the  second  column. 

QUESTIONS. — 1.  What  inference  can  you  draw  regarding 


CANDLE-POWER  BY  THE  RVMFORD  PHOTOMETER.  199 

the  relations  of  distance  and  degree  of  radiation  ?  2.  If 
D  and  Dr  be  any  two  distances,  and  I  and  1'  the  corre- 
sponding intensities,  can  you  combine  them  in  a  formula  ? 
Eemember  that  for  each  distance  the  same  amount  of  light 
will  spread  over  a  surface  whose  area  would  be  proportional 
to  the  squares  of  the  width  of  the  square  of  light,  and  that 
the  intensity  of  the  light  will  become  less  in  proportion  to 
the  surface  illuminated. 

EXERCISE  4. 

CANDLE-POWER  BY  THE  RUMFORD  PHOTOMETER. 

Preliminary. — The  unit  used  in  comparing  the  light-in- 
tensities is  called  one  candle-power,  written  c.  p.  Candle- 
power  is  measured  by  determining  the  distances  at  which 
the  source  of  light  to  be  tested,  and  a  standard  candle 
specified  by  law,  give  lights  of  equal  intensity.  For  ex- 
ample, if  the  light  to  be  measured  and  the  standard  candle 
must  be  at  the  same  distance  in  order  to  give  light  of 
equal  intensity,  the  light  of  required  intensity  would  be 
1  c.  p. 

The  form  of  photometer  used  in  this  exercise  is  shown 


FIG.  101. 


in  Fig.  101,  and  is  called  the  Rumford  Photometer.  Two 
meter-sticks  MM  carry  two  blocks  LL'9  one  of  which 
supports  the  standard  reference-candle,  the  other  the  light 
to  be  measured,  represented  here  by  two  candles.  These 


200 


LIGHT. 


blocks  can  be  moved  to  any  position  on  the  meter-sticks. 
A  card-board  screen  8'  is  placed  between  them,  and  an  up- 
right rod  R  at  the  left-hand  ends  of  the  meter-sticks.  Each 
light  will  cast  a  shadow  from  this  rod  upon  the  screen  at 
the  left.  When  these  shadows  are  equally  black,  both  lights 
are  of  equal  intensity  at  the  screen. 

EXPERIMENT. 

Apparatus.—  Rumford  photometer  as  in  Fig.  101;  candle;  light  to 
be  tested;  scissors. 

OBJECT. — To  determine  the  candle-power  of  a  light  by 
the  Rumford  photometer. 

MANIPULATION. — Place  one  candle  on  block  L',  light  it, 
and  set  the  block  30  cm.  from  the  rod.  Place  on  L  the 
light  to  be  tested.  Allow  the  lights  to  burn  for  a  few 
moments,  and  then  move  L  towards  the  screen  until  the 
two  shadows  cast  by  the  rod  are  equally  dark.  Read  the 
position  of  the  right-hand  side  of  L.  Move  L  towards  the 
screen  until  its  shadow  is  decidedly  the  darker  (recollect 
that  the  shadows  cross),  then  move  it  towards  the  right 
until  the  shadows  are  equal,  and  again  record  the  reading 
of  L.  Move  L'  10  cm.  nearer  R  and  repeat.  Repeat  again 
with  L'  10  cm.  still  nearer.  Record  as  follows: 


Pos.  of  L'. 

True  Pos.  of 
Candle. 

Pos.  of  L. 

True  Pos.  of 
Light.* 

Dist.  from 
Screen  to* 
Candle. 

Dist.  from 
Screen  to 
Light. 

R. 

L. 

Av. 

CALCULATION. — Using  the  formula  of  Ex.  2,  all  the 
values  are  given  in  the  table  above,  except  the  intensity 
of  the  light  to  be  tested,  the  intensity  of  the  candle  L' 
being  taken  as  1  c.  p.  Substitute  these  values  for  each 
case,  taking  the  intensity  of  the  light  to  be  tested  as  X. 
Average  the  values  so  obtained,  and  put  them  down  as 
candle-power. 

*  Distances  of  L  and  L'  from  rod,  plus  distance  of  rod  from  screen. 


SOUND. 
EXERCISE  1. 

CONDITIONS  AFFECTING  PITCH. 

Preliminary. — The  following  exercise  investigates  the 
conditions  affecting  the  pitch  of  the  note  given  by  the 
vibrating  wire.  For  this  purpose  the  apparatus  shown  in 

^ VT iA^oem 

c»A/^ 

^^^^ 


FIG.  102. 

Fig.  102  is  used.  The  wires  WW  of  different  sizes  are 
stretched  by  the  balances  BB'f  the  lengths  used  being 
those  between  the  triangular  blocks  CC'.  In  order  that 
the  tension  may  be  the  same  for  different  lengths,  a  fifth 
block,  D,  may  be  placed  under  the  string,  the  wire  being 
pressed  down  on  D  by  the  finger  H}  as  shown  in  the  figure. 
Cords  cc  wound  around  nails  aa  hold  the  balances  at  any 
desired  tension. 

EXPERIMENT. 

Apparatus.— As  in  Fig.  102.    Meter-stick. 

OBJECT. — To  observe  the  effect  of  (a)  length,  (b)  tension, 
(c)  size,  on  the  pitch  of  the  note  given  by  a  stretched  wire. 

MANIPULATION. — Part  L  The  apparatus  being  arranged 
as  in  Fig.  102,  hold  balance  B  in  the  left  hand,  take  a  turn 
of  the  cord  c  around  the  right-hand  nail  a,  steadily  pull  to 
the  left  on  B,  and  at  the  same  time  pulling  the  cord  with 
the  right  hand  until  B  reads  8  Ibs.  Eemove  the  left  hand, 
and  let  the  whole  strain  come  upon  the  cord.  Make  the 
cord  fast  by  four  or  five  crossed  turns  around  both  nails. 

201 


202 


SOUND. 


If  the  cord  stretches  so  that  the  tension  drops  below  8  Ibs., 
the  operation  must  be  repeated.  In  like  manner  put  W 
under  the  same  tension.  Bring  D  close  to  the  left-hand 
block  C\  measure  the  length  of  wire  between  D  and  right- 
hand  block  by  laying  the  meter-stick  on  the  blocks  parallel 
to  the  wire.  Press  the  finger  on  the  wire  to  the  left  of  D, 
as  at  H  in  Fig.  102,  and  sound  W.  Shorten  W  by  moving 
D  to  the  right,  and  look  for  positions  that  give  the  first  and 
second  octaves  of  the  note  first  obtained,  measuring  the 
length  in  each  case.  Move  D  back  to  its  original  position, 
and  calling  the  note  given  by  W  "  do  "  on  the  scale,  look 
for  positions  giving  the  other  notes  in  the  gamut.  If  pos- 
sible, carry  these  measurements  through  the  second  octave. 
Repeat,  starting  with  a  different  length.  Record  as  follows: 


TABLE  I. 


Tension. 

Length. 

Note. 

Part  II.  Remove  Z>,  sound  W,  and  change  the  length 
of  W  so  that  it  gives  the  same  note  as  W.  Then  find  what 
tension  on  one  half -length  of  W  will  give  the  same  note  as 
W.  The  note  given  by  W  is  simply  used  as  a  reference  ; 
hence  the  length  of  W  need  not  be  recorded.  Shorten  W 
10  cm.  by  moving  the  block  D,  again  set  B  at  8  Ibs.,  and 
repeat  the  whole  operation.  Do  this  for  several  lengths, 
and  record. 

TABLE  II. 


1st  Tension  of  W. 

Tension  of  W  for  same 
Note  on  7iaZ/-length. 

Note  that  whole-length 
of  W  would  give.* 

*  See  Part  I. 


VELOCITY  OF  SOUftfi. 


203 


Part  III.  With  a  tension  of  8  Ibs.  on  each  string,  and 
with  equal  length  of  wire,  compare  the  notes.  Do  this  for 
several  lengths  and  tensions.  Eecord 


TABLE  III. 


Length  W. 

Length  W. 

Tension  TFand  W. 

Pitch  of  note. 

QUESTIONS. — 1.  Can  you  make  out  any  relation  between 
the  length  giving  any  note  and  that  giving  its  octave? 
2.  Do  the  lengths  giving  the  note  on  the  scale  bear  any 
definite  relations  to  the  length  giving  the  first  note  ?  If 
so,  what  ?  3.  Can  you  make  out  any  connection  between 
tension  and  pitch  ?  4.  Between  size  and  pitch  ?  5.  Name 
some  musical  instruments  in  which  these  principles  are 
used,  and  explain  how  they  are  applied. 

EXERCISE  2. 

VELOCITY  OF  SOUND. 

Preliminary. — In  the  following  exercise  the  velocity  of 
sound  is  determined  in  two  media — air  and  carbon  dioxide. 
The  method  used  is  based  upon  the  fact  that  if  a  tuning- 
fork  be  sounded  at  the  mouth  of  a  tube  closed  at  one  end, 
the  length  of  the  air-column  which  will  reinforce  the  sound 
of  the  fork  is  one  quarter  the  wave-length.  By  using 
a  fork  of  known  number  of  vibrations,  and  finding  by 
trial  the  length  of  air-column  which  will  respond  to  the 
fork,  the  velocity  may  be  calculated. 

EXPERIMENT. 

Apparatus.— Resonant  tube;  tuning-fork;  wash  -  bottle  with 
water  ;  chemical  generator  ;  marble  ;  muriatic  acid  ;  meter-stick ; 
blocks  of  wood  to  support  generator  ;  thermometer. 

OBJECT. — To  determine  the  velocity  of  sound,  (a)  in  air, 
(l>)  in  carbon  dioxide. 


204 


60VND. 


MANIPULATION". — The  tube  being  placed  upon  a  firm 
surface,  sound  the  fork  holding  it  horizontally  over  its 
mouth,  one  prong  directly  above  the  other.  By  means  of 
the  wash-bottle,  run  water  into  the  tube  until  the  point  of 
strongest  reinforcement  is  found.  When  this  point  is  ap- 
proached, add  the  water  very  cautiously,  holding  the  deliv- 
ery-tube of  the  bottle  close  against  the  sides  of  the  tube, 
taking  care  to  wet  the  sides  of  the  tube  as  little  as  possible. 
Place  the  meter-stick  against  the  inner  wall  of  the  tube, 
and  measure  the  distance  from  the  level  of  the  water  to  the 
top  of  the  tube.  Pour  out  some  of  the  water  and  repeat, 
making  four  or  five  trials  in  all.  Empty  the  tube  com- 
pletely, and  support  the  generator  on  blocks  so  that  the  end 
of  the  delivery-tube  reaches  nearly  to  the  bottom  of  the 
tube.  Pour  about  20  cm.  of  acid  into  the  generator  and 
allow  it  to  run  for  three  or  four  minutes;  then  proceed  as 
above.  Kecord  the  temperature.  Tabulate  : 


Substance  used. 

Length  of  air-column. 

Average. 

CALCULATION. — Average  separately  the  values  of  the 
quarter  wave-length  obtained  for  air  and  for  carbon  di 
oxide.     By  substituting  these  values  and  the  number  of 
vibrations  of  the  fork  in  the  formula 
V  =  No.  of  vibr.  X  4  (length  of  air-col.  +  J-  diam.  of  tube) 
calculate  the  velocity  of  sound  in  each  medium. 


INDEX. 


^-  Numbers  above  204  refer  to  teachers'  edition. 


Abbreviations,  metric,  59 

Absorption  and  radiation,  150; 
exp.  151;  app.  218;  notes  and 
ref.  268 

Action  of  acid  on  bodies,  exp. 
17;  attracted  body  on  magnet, 
4;  exp.  5;  notes  and  ref.  256; 
currents  on  magnets,  exp.  25; 
notes  and  ref.  257;  force,  exp. 
153;  app.  220,  247;  notes  and 
ref.  269;  magnet  free  to  move, 
exp.  5 

Action  and  reaction,  6;  exp.  178, 
179;  app.  Ill,  180,  220,  249; 
notes  and  ref.  271 

Ampere's  law,  27;  exp.  on,  25 

Angular  forces,  composition  and 
resolution  of,  160 

Apparatus,  6,  207;  construction 
of:  density  and  specific  gravity, 
242;  dynamics,  247;  electricity, 
225;  heat,  244;  light,  252; 
magnetism,  224;  mensuration, 
237;  sound,  254;  lists  of:  den- 
sity and  specific  gravity,  217; 
dynamics,  220;  electricity,  214; 
heat,  218;  light,  222;  magnet- 
ism, 214;  mensuration,  216; 
sound,  222 

Archimedes'  principle,  exp.  93; 
notes  and  ref.  261 

Atmospheric  pressure,  exp.  107; 
app.  217,  243;  notes  and  ref. 


Balance,     79,     217,     238,    239; 

spring,  82,  85,  217,  219,  220; 

substitute  for,  247 
Battery,  30;  fluid,  215,  227 
Binding-posts,    223;    substitute, 

230;  English,  231 
Boiling-point,    exp.     126;    notes 

and  ref.  267 
Boyle's  law,  185;  exp.  186;  app. 

185,    220,    250;    notes  and  ref. 

271 ;  calibration  of  tube,  251 
Breaking    circuit,   29;  magnets, 

exp.  8;  notes  and  ref.  256 
Bunsen  burner,    112,  218;    pho- 
tometer, 194 
Burette,  71,  216;  substitute,  237 

Calibration  of  a  tube,  146,  251 
Calorie,  129 
Calorimeter,  130,  218 
Caudle-power,     199;    exp.    200; 

app.  199,  222,  254 
Cell:  see  Galvanic  Cell. 
Cells,    methods  of    connecting, 

exp.  36;  notes  and  ref.  258 
Centre  of  gravity,  of  pendulum, 

175 

Changing  systems  of  units,  58 
Chemical  change,  exp.  87;  notes 

and  ref.     261;    thermometer, 

117,  218 

Circuit,  24;  introducing  into,  29 
Coefficient  of  cubical  expansion, 

139;  gas,    exp.  146;  app.   218, 
205 


206 


244;  notes  and  ref.  261 ;  liquid, 
exp.  145;  app.  218,  245;  notes 
and  ref.  261;  linear  expansion, 
188;  exp.  140,  141;  app.  139, 
142,  218,  246;  notes  and  ref. 
268 

Coils  of  wire,  32,  214,  232 

Components,  160;  of  angular 
forces,  160;  parallel  forces, 
166 

Compass,  6,  7;  substitute,  214, 
224 

Composition  of  angular  forces, 
160;  exp.  162;  app.  220,  247; 
notes  and  ref.  270;  parallel 
forces,  exp.  166;  app.  220,  248; 
notes  and  ref.  270 

Conductors,  24;  in  series  or  par- 
allel, 33 

Conduction  of  heat,  116 

Conjugate  focal  length,  193 

Constant  errors,  85 

Conditions  affecting  electrical 
resistance,  29;  exp.  30;  app.  32, 
214,  232;  notes  and  ref.  257; 
pitch,  exp.  201;  app.  201,  222, 
254;  notes  and  ref.  272 

Connector,  215 

Convection,  116 

Cost  of  equipment,  207 

Counterpoising,  82 

Cross-section  of  tube,  exp.  76; 
app.  216;  notes  and  ref.  260 

Current,  electric,  20,  24;  revers- 
er,  225 

Currents,  induced,  52;  exp.  53; 
app.  52,  214;  notes  and  ref.  259 

Curve  plotting,  122,  124 

Density,  89;  unit  of,  91;0zp.  90; 
app.  217;  notes  and  ref.  261; 
and  specific  gravity,  app.  con- 
struction, 242;  lists,  217;  notes 
and  ref.  261 

Determination  of  length,  59,  62; 
volume,  67;  diameter  of  a 
sphere,  61 

Diagrams,  21 

Direction  of  current,  24 

Distance  and  intensity  of  light, 
194;  exp.  195;  app.  195,  222, 
252;  notes  and  ref.  272 


Distribution  of  heat  in  a  rod, 
exp.  114;  of  magnetism,  2 

Dynamics,  Exercise  1,  153;  notes 
and  ref.  269;  construction, 
247;  list  of,  220 

Dynamo,  54;  model,  233 

Dynamometer,83;  substitute,  247 

Edison  current,  208;  uses  of,  210 
Elasticity,  force  of,  183;  of  a  gas, 
186  (see  Boyle's  law);  of  a 
solid,  exp.  184;  app.  183,  220, 
252;  notes  and  ref.  271;  spe- 
cific gravity  by  exp.  190;  app. 

190,  220,  252 

Electricity,  17;  construction, 225; 
lists  of,  214 

Electro-magnetism,  exp.  50;  app. 
214;  notes  and  ref.  259 

Electro-motive  force,  49;  exp.  48; 
app.  214;  notes  and  ref.  259; 
standard,  49 

Electric  current,  20;  circuit,  29 

Electrical  resistance,  33;  exp.  34; 
notes  and  ref.  258;  conditions 
affecting  exp.  29;  relative,  40 

Elements  of  cell,  23 

English  units,  57;  measure,  57 

Equilibrium,  156 

Equipment,  cost  of,  207;  gen- 
eral, 223 

Errors,  85 

Essays,  206 

Exciting  fluid,  23 

Expansion,  suggestions  for  illus- 
trating, 265;  coefficients  of,  139 

Field  of  magnet,  12 

Float,  72 

Focal  length  of  lenses,  191 

Focii  of  lenses,   exp.   191;  app. 

191,  222,  252;  notes  and  ref.  271 
Focus  of  lens,  191 

Force,  4,  269;  action  on  a  body, 
153;  composition  of,  160;  exp. 
162,  166;  notes  and  ref.  270; 
form  of  lines  of,  15;  graphical 
representation  of,  158;  measure- 
ment of,  157;  of  elasticity,  in 
a  solid,  183;  exp.  184;  notes  and 
ref.  271;  in  a  gas,  exp.  186; 
notes  and  ref.  271;  of  friction, 


207 


156;  exp.  156;  app.  220,  247; 
notes  and  ref.  269;  of  tenacity, 
exp.  181;  notes  and  ref.  271 

Forces,  direction  indicated  by 
signs,  159;  geometrical  addi- 
tion and  subtraction  of,  159; 
by  algebra,  159;  parallelogram 
of,  163;  exp.  164;  parallel, 
composition  of,  166 

Formula  for  changing  system  of 
linear  units,  58,  186;  cubical 
coefficient  of  a  gas,  150;  den- 
sity, 90;  diameter  of  circle 
from  area,  78;  heat  quantity, 
129;  latent  heat,  186,  137;  lin- 
ear coefficient  of  expansion,  141, 
144;  number  grins,  in  an  oz., 
83;  number  ins.  in  a  meter,  63; 
specific  gravity  by  elasticity, 
190;  by  moments,  189;  of  li- 
quids, 93;  by  balancing,  104, 
106,  109;  of  solids,  97,  98; 
specific  heat,  132,  133;  work 
(inclined  plane),  172 

French  units,  57 

Friction,  force  of,  156 

Galvanic  cell,  23;  diagram  of, 
24;  direction  of  current  in,  24; 
construction  of,  214,  227,  236 

Galvanometer,  27;  construction 
of,  215,  229;  diagram  of,  28; 
precautions,  28;  sensitive,  215, 
231 

Gas,  temporary  piping,  211 

Gases,  elasticity  of  (see  Boyle's 
law),  185 

General  laboratory  equipment, 
211,  223;  method,  34,  205;  sug- 
gestions, 205,  Preface;  study  of 
a  magnet,  exp.  1;  app.  214; 
notes  and  ref.  256 

Glass  cutting,  208 

Graduated  cylinder,  67;  use,  70; 
flask,  72 

Graphical  representation  o  f 
forces,  158;  of  results,  122 

Heat,  app.  218;  construction,  244; 
notes  and  ref.  264;  capacity, 
127,  exp.  127;  app.  218,  notes 
and  ref.  269;  conduction  of, 


116;  how  it  travels,  exp.  113; 
app.  113,  218;  notes  and  ref. 
265;  radiation  of,  116;  specific, 
128 
Heating,  precautions  in,  113 

Induction,  6 

Induced  magnetism,  exp.  8;  notes 

and  ref.  256;  currents,  exp.  52; 

app.  216;  notes  and  ref.  259 
Inducing  magnet,  10 
Inclined  plane,    169;  exp.    170; 

app.  170,  220, 248;  notes  andref. 

270;  as  wedge  and  screw,  173 
Intensity  of  light,  194 
Irregular  body,  volume  of,  exp. 

74 

Laboratory  work,  preparation  of, 
207,  Preface;  equipment,  223 

Latent  heat,  133;  exp.  134,  137; 
app.  134,  219,  224;  notes  and 
ref.  267 

Law,  6;  of  cooling,  exp.  124; 
notes  and  ref.  266;  of  induced 
poles,  exp.  8;  magnets,  10;  notes 
and  ref.  256;  of  magnet,  6 

Lectures,  206 

Length,  determination  of,  59; 
units  of,  56;  of  pendulum,  175; 
units  of,  57 

Lenses,  focal  length,  193;  conju- 
gate, 193 

Light,  app.  construction,  252; 
list,  222;  notes  andref.  271;  in- 
tensity of,194;  effect  of  distance 
on,  exp.  195;  app.  195,  222, 
253;  notes  and  ref.  272;  radia- 
tion of,  197;  exp.  197;  app. 
222,  253;  notes  and  ref.  272; 
unit  of,  199;  exp,  200;  app.  199, 
222,  254;  notes  and  ref.  272 

Lines  of  magnetic  force,  12;  exp. 
13;  app.  214;  notes  and  ref.  256 

Lin  ear  measurements,  57;  scales, 
English,  59;  French,  59;  read- 
ing, 60;  pracitce  in  use  of,  exp. 
62 

Liquid  pressure  due  to  weight, 
99;  exp.  100;  app.  217,  242; 
notes  andref.  262;  weighing, 
81 


208 


INDEX. 


Machines,  169 

Magnet,  general  study  of,  exp  A; 

bar,  2;  action  of  attracted  body 

on,  exp.  4;  of  currents  on,  exp. 

25;  notes  and  ref.  257 
Magnets,  breaking,  exp.  8;  notes 

and  ref.  256;  law  of,  induced, 

exp.   10;    notes  and  ref.    256; 

mutual  action  of  two,  exp.  6; 

notes  and  ref.  256 
Magnetism,  app.  224;   lists,  214; 

induced,  exp.  8;  notes  and  ref. 

256 
Magnetic  force,  lines  of,  exp.  12; 

field,  12;  poles,  6 
Measurement,  of  forces,  157;  of 

resistance,   exp.    42,   45;    app. 

226;  notes  and  ref.  258;  notes 

on,  56 
Measuring  vessels,   67,    71,   72; 

substitutes,  237 
Melting  point,  exp.  125;  notes  and 

ref.  267;  tubes,  125 
Meniscus,  68 
Mensuration,  app.  237;  notes  and 

ref.  260;  list,  216 
Mercury,  214,  218,  220;  care  of, 

210;  calibration  by,  237,  251; 

cups,  214,  230 
Meter,  57;  sticks,  216 
Metric  system,  57;  abbreviations, 

59;  units,  57;  values,   estima- 
tion of,  exp.  84;  notes  and  ref. 

261;  weights,  79 
Moment  of  a  force,  169;  specific 

gravity  by,  exp.  189 
Motor,  principle,  exp.  54;  model, 

233 
Multiple  arc,  33 

Naming  of  poles,  6 
Notes,  form  of,  205;  on  errors, 
85;  on  measurement,  56 

Ohm.39 

Parallel  forces,  exp.  166 

Pendulum,  exp.  174;  app.  174, 
220;  notes  and  ref.  270 

Personal  errors,  85 

Phenomenon,  2 

Photometer,  Bunsen,  194;  Rum- 
ford,  199 


Physical  and  chemical  change, 
exp.  86;  notes  and  ref.  261;  app. 
216 

Plates,  positive  and  negative,  24 

Polarity,  3,  4 

Poles,  4;  naming,  6;  action  of  one 
on  another,  6;  induced,  exp. 
8 ;  law  of,  exp.  10 

Practice  in  determining  volume, 
exp.  62;  app.  216;  notes  and  rej. 
260;  estimating  metric  values 
exp.  84;  notes  and  ref.  261;  use 
of  linear  scales,  exp.  62;  app. 
216;  notes  and  ref.  260;  weigh- 
ing, exp.  83;  app.  216;  notes 
and  ref.  261 

Qualitative  experiment,  4 
Quantitative  experiment,  4 

Rack  with  wires,  41,  215,  231 

Radiation  of  heat,  116;  and  ab- 
sorption, 150;  exp.  151;  app. 
218;  notes  and  ref.  268;  of  light, 
197;  exp.  197;  app.  222,  253; 
notes  and  ref.  272 

Ratio,  89 

Reading  by  reversal,  29;  linear 
scales,  61;  pointer  against 
scale,  62;  volumes,  68 

Relation  of  circumference  to  di- 
ameter, exp.  64;  app.  216;  notes 
and  ref.  260 

Relative  resistance,  exp.  40;  app. 
41,  215,  231;  notes  and  ref.  258 

Residual  magnetism,  10 

Resistance,  40;  unit  of,  39;  con- 
ditions affecting,  29,  33;  meas- 
urement of,  exp.  42,  45;  box, 
39,  40,  215,  225 

Retentivity  of  steel,  10 

Resultant,  160;  of  forces,  exps. 
162,  166 

Reverser,  215,  225 

Rheostat,  39,  208 

Scales,  linear,  57;  balances,  79, 
217;  substitutes;  239;  of  spring 
balances,  82 

Sections,  size  of,  208 

Solution,  exp.  152;  notes  and  ref. 
268 


200 


Sound;  app.  254;  list,  222;  notes 
and  ref.  272;  pitch  of,  exp.  201; 
velocity  of,  exp.  203 

Special  method,  34,  205;  con- 
dition of  wire,  20 

Specific  gravity,  of  a  liquid,  by 
bottle,  92;  exp.  92;  app.  217; 
notes  and  ref.  261;  balancing, 
103;  exp.  104;  app.  205,  217, 
243;  notes  and  ref.  263;  atmos- 
pheric tension,  109;  exp.  109; 
app.  110,  217,  243;  notes  and 
ref.  264;  by  floating  body,  exp. 
107;  app.  217;  notes  and  ref. 
263,  of  solids.  96;  exp.  96;  app. 
217;  notes  and  ref.  262;  bottle, 
93,  94,  217;  without  scales  or 
weights,  exp.  189;  app.  220, 
252;  notes  and  ref.  271 

Specific  heat,  128,  129;  exp.  130; 
app.  218 ;  notes  and  ref.  267 

Spring  balance,  82,  217,  220; 
error,  85;  substitute,  247 

Square  measure,  58 

Sulphate  of  copper  cell,  236,  259 

Substitutes,  balances,  239;  bind- 
ing post,  230;  compasses,  224; 
dynamometer,  247;  measuring 
vessels,  237;  weights,  241 

Support,  for  apparatus,  251 

Surface  measure,  58 

T  square,  171,  220 
Temperature,  116;  and  physical 

form,  119;  exp.  120;  app.  119, 

218;  notes  and  ref.  266 
Tenacity,  exp.  181 
Testing  thermometers,  exp.  118; 

app.   218,  244;  notes  and  ref, 

265 
Thermometers,    117,    218,    244; 

wps.  266 


Tumbler  cell,  23,  215,  237 
True  focal  length,  193 

Unit  of  force,  158;  of  length,  57; 

of  surface,  58;  of  volume,  58; 

of  measure,   56;  English,    57; 

French,  57;  change  from  one 

system  to  another,  57;  theory 

of,  56. 
Useful  books,  212 

Velocity  of  sound,  exp.  203;  app. 
222;  notes  and  ref.  272 

Vibration  of  pendulum,  exp.  174, 
wires,  exp.  201 

Voltaic  electricity,  17;  produc- 
tion, exp.  18;  notes  and  ref. 
257 

Volume,  units,  58;  scales,  67,  71; 
practice  in  determination  of,  74 

Weighing,  proper  method  of,  80; 
of  liquids,  81;  solid  in  liquid, 
95;  by  counterpoising,  82 

Weight,  units  of,  78;  determina- 
tion of,  78;  by  spring  balance, 
82;  in  chemical  and  physical 
change,  86;  liquid  pressure  due 
to,  exp.  99;  apparatus  for,  99, 
217,  242;  of  liquid  displaced  by 
floating  body,  exp.  on  106;  app. 
217;  notes  and  ref.  260;  lost  by 
a  body  immersed  in  a  liquid, 
93;  exp.  94;  notes  and  ref.  261 

Weights,  79,  217,  241 

Wheatstone's  bridge,  measure 
ment  of  resistance  by,  45;  app 
215,  225; 

Wire,  223;  coils  of  214,  232, 
rack  with,  214,  231 

Zinc,  amalgamated,  18 


YB  36012 


